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- Question 1 and 2 Exercise 6.1
- Question 3 & 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 1 and 2 Exercise 6.2
- Question 3 and 4 Exercise 6.2
- Question 5 and 6 Exercise 6.2
- Question 7 and 8 Exercise 6.2
- Question 9 Exercise 6.2
- Question 10 Exercise 6.2
- Question 11 Exercise 6.2
- Question 12 Exercise 6.2
- Question 13 Exercise 6.2
- Question 14 and 15 Exercise 6.2
- Question 1 Exercise 6.3
- Question 2 Exercise 6.3
- Question 3 Exercise 6.3
- Question 4 Exercise 6.3
- Question 5 and 6 Exercise 6.3
- Question 7 and 8 Exercise 6.3
- Question 9 Exercise 6.3
- Question 9 Exercise 6.3
- Question 1 Exercise 6.4
- Question 2 Exercise 6.4
- Question 3 Exercise 6.4
- Question 4 Exercise 6.4
- Question 5 Exercise 6.4
- Question 6 Exercise 6.4
- Question 7 Exercise 6.4
- Question 1 and 2 Exercise 6.5
- Question 3 and 4 Exercise 6.5
- Question 5 and 6 Exercise 6.5
- Question 7 Exercise 6.5
- Question 8 Exercise 6.5
- Question 9 Exercise 6.5
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- Question 1 Review Exercise 6
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- Question 7 & 8 Review Exercise 6
- Question 9 & 10 Review Exercise 6
- Question 11 Review Exercise 6
Fulltext results:
- Question 7 Exercise 6.4
- ====== Question 7 Exercise 6.4 ====== Solutions of Question 7 of Exercise 6.4 of Unit 06: Permutation, ... obability of getting doublet of even numbers. ====Solution==== The sample space rolling a pair of dice ... probability of getting a sum less than $6$. ====Solution==== The sample space rolling a pair of dice ... e probability of getting a sum more than $7.$ ====Solution==== The sample space rolling a pair of dice
- Question 1 and 2 Exercise 6.2
- ====== Question 1 and 2 Exercise 6.2 ====== Solutions of Question 1 and 2 of Exercise 6.2 of Unit 06: P... n. =====Question 1(i)===== Evaluate $^6 P_6$ ====Solution==== \begin{align}^6 P_6&=\dfrac{6 !}{(6-6) !... =====Question 1(ii)===== Evaluate $^{20} P_2$ ====Solution==== \begin{align}^{20} P_2&=\dfrac{20 !}{(20... ====Question 1(iii)===== Evaluate $^{16} P_3$ ====Solution==== \begin{align}^{16} P_3&=\dfrac{16 !}{(16
- Question 1 and 2 Exercise 6.1
- ====== Question 1 and 2 Exercise 6.1 ====== Solutions of Question 1 and 2 of Exercise 6.1 of Unit 06: P... aluate the $\dfrac{10 !}{3 ! .3 ! \cdot 4 !}$ ====Solution==== \begin{align}\dfrac{10 !}{3 ! \cdot 3 ! ... ===== Evaluate the $\dfrac{3 !+4 !}{5 !-4 !}$ ====Solution==== \begin{align}\dfrac{3 !+4 !}{5 !-4 !}&=\... ===== Evaluate the $\dfrac{(n-1) !}{(n+1) !}$ ====Solution==== \begin{align}\dfrac{(n-1) !}{(n+1) !} &=
- Question 13 Exercise 6.2
- ====== Question 13 Exercise 6.2 ====== Solutions of Question 13 of Exercise 6.2 of Unit 06: Permutation... these permutations begin with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellen... with $\mathrm{E}$ and end with $\mathrm{C}$ ? ====Solution==== The total number of letters in 'Excellen... with $\mathrm{E}$ and end with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellen
- Question 4 Exercise 6.4
- ====== Question 4 Exercise 6.4 ====== Solutions of Question 4 of Exercise 6.4 of Unit 06: Permutation, ... at is the probability of obtaining all heads? ====Solution==== First we construct a tree diagram to fin... at is the probability of obtaining two heads? ====Solution==== First we construct a tree diagram to fin... hat is the probability of obtaining one hcad? ====Solution==== First we construct a tree diagram to fin
- Question 1 Exercise 6.3
- ====== Question 1 Exercise 6.3 ====== Solutions of Question 1 of Exercise 6.3 of Unit 06: Permutation, ... TBB) Peshawar, Pakistan. =====Question 1(i)===== Solve $^n C_2=36$ for $n$. ====Solution==== We are given: \begin{align}&^n C_2=36\\ & \Rightarrow \dfrac{... erefore, we have $n=9$. =====Question 1(ii)===== Solve $^{n+1} C_4=6,^{n-1} C_2$ for $n$. ====Solution
- Question 3 & 4 Exercise 6.1
- ====== Question 3 & 4 Exercise 6.1 ====== Solutions of Question 3 & 4 of Exercise 6.1 of Unit 06: Permu... dfrac{2}{7 !}+\dfrac{3}{8 !}=\dfrac{75}{8 !}$ ====Solution==== We are taking the L.H.S of the above giv... ve that $\dfrac{(n+5) !}{(n+3) !}=n^2+9 n+20$ ====Solution==== We are taking the L.H.S of the above giv... ac{n(n !)}{(n-5) !}=\dfrac{12(n !)}{(n-4) !}$ ====Solution==== We are given: \begin{align}\dfrac{n(n !)
- Question 12 Exercise 6.2
- ====== Question 12 Exercise 6.2 ====== Solutions of Question 12 of Exercise 6.2 of Unit 06: Permutation... WORM" if the letters are taken all at a time? ====Solution==== BOOKWORM\\ The total number of letters i... EPER" if the letters are taken all at a time? ====Solution==== BOOKKEEPER\\ The total number of letters... ABAD" if the letters are taken all at a time? ====Solution==== ABBOTABAD\\ Total number of letters are
- Question 1 Exercise 6.4
- ====== Question 1 Exercise 6.4 ====== Solutions of Question 1 of Exercise 6.4 of Unit 06: Permutation, ... e. What is the probability of rolling a $5$ ? ====Solution==== Rolling a $5$ Let \begin{align}A&=\{5\}\... obability of rolling a number less than $1$ ? ====Solution==== Rolling a number less than $1$ Let \begi... bility of rolling a number greater than $0$ ? ====Solution==== Rolling a number greater than $0$ Let \b
- Question 3 Exercise 6.4
- ====== Question 3 Exercise 6.4 ====== Solutions of Question 3 of Exercise 6.4 of Unit 06: Permutation, ... the probability that $8$ answers are correct. ====Solution==== We have $8$ questions, each question has... the probability that $7$ answers are correct. ====Solution==== We have $8$ questions, each question has... the probability that $6$ answers are correct. ====Solution==== We have $8$ questions, each question has
- Question 6 Exercise 6.4
- ====== Question 6 Exercise 6.4 ====== Solutions of Question 6 of Exercise 6.4 of Unit 06: Permutation, ... obability of each of the Drawing an ace card. ====Solution==== Total cards $$=52$$ An ace. Total ace ca... f each of the Drawing either spade or hearıs. ====Solution==== Total cards $=52$ Drawing either space ... bility of each of the Drawing a diamond card. ====Solution==== Total cards $=52$ Drawing a diamond car
- Question 9 Exercise 6.5
- ====== Question 9 Exercise 6.5 ====== Solutions of Question 9 of Exercise 6.5 of Unit 06: Permutation, ... d the probability that both will be selected. ====Solution==== \begin{align} P(\text { Ajmal scicction ... nd the probability that Only one is selected. ====Solution==== \begin{align} P(\text { Ajmal scicction ... d the probability that none will be sclected. ====Solution==== \begin{align} P(\text { Ajmal scicction
- Question 7 & 8 Review Exercise 6
- ====== Question 7 & 8 Review Exercise 6 ====== Solutions of Question 7 & 8 of Review Exercise 6 of Unit... )=0.5$ and $P(B / A)=0.4$, find $P(A \cap B)$ ====Solution==== We know that: \begin{align} P(B \mid A)&... P(B)=0.5$ and $P(B / A)=0.4$, find $P(A / B)$ ====Solution==== We know that $$P(A \mid B)=\dfrac{P(A \c... )=0.5$ and $P(B / A)=0.4$, find $P(A \cup B)$ ====Solution==== \begin{align} P(A \cup B)&=P(A)+P(B)-P(A
- Question 3 and 4 Exercise 6.2
- ====== Question 3 and 4 Exercise 6.2 ====== Solutions of Question 3 and 4 of Exercise 6.2 of Unit 06: P... nciple of counting $^n P_r=n(^{n-1} P_{r-1})$ ====Solution==== We are given that: $$^n P_r=n({ }^{n-1} ... ounting $^n P_r=^{n-1} P_r+r(^{n-1} P_{r-1})$ ====Solution==== We are given: $$^n P_r=^{n-1} P_r+r({ }^... partment arrange eight suspects in a line up? ====Solution==== The total number of suspects are eight s
- Question 7 and 8 Exercise 6.2
- ====== Question 7 and 8 Exercise 6.2 ====== Solutions of Question 7 and 8 of Exercise 6.2 of Unit 06: P... igits $1,2,3,4$ and 5 if repetitions allowed? ====Solution==== There are three places (hundred digit, t... ,2,3,4$ and 5 if repetitions are not allowed? ====Solution==== If repetition is not allowed then each d... n" if all the vowels are to be kept together? ====Solution==== The total number of alphabets in word eq