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- Question 7 Exercise 6.4
- obability of getting doublet of even numbers. ====Solution==== The sample space rolling a pair of dice is \b... probability of getting a sum less than $6$. ====Solution==== The sample space rolling a pair of dice is \b... e probability of getting a sum more than $7.$ ====Solution==== The sample space rolling a pair of dice is \b... bability of getting a sum greater than $10.$ ====Solution==== The sample space rolling a pair of dice is \b
- Question 1 and 2 Exercise 6.1
- aluate the $\dfrac{10 !}{3 ! .3 ! \cdot 4 !}$ ====Solution==== \begin{align}\dfrac{10 !}{3 ! \cdot 3 ! \cdot... ===== Evaluate the $\dfrac{3 !+4 !}{5 !-4 !}$ ====Solution==== \begin{align}\dfrac{3 !+4 !}{5 !-4 !}&=\dfrac... ===== Evaluate the $\dfrac{(n-1) !}{(n+1) !}$ ====Solution==== \begin{align}\dfrac{(n-1) !}{(n+1) !} &= \df... iv)===== Evaluate the $\dfrac{10 !}{(5 !)^2}$ ====Solution==== \begin{align}\dfrac{10 !}{(5 !)^2}&=\dfrac{10
- Question 1 and 2 Exercise 6.2
- 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 !}{(20-2) !... ====Question 1(iii)===== Evaluate $^{16} P_3$ ====Solution==== \begin{align}^{16} P_3&=\dfrac{16 !}{(16-3) !... 2(i)===== Solve $^n P_5=56(^n P_3)$ for $n.$ ====Solution==== We are given: \begin{align}^n P_5&=56(^n P_3)
- Question 13 Exercise 6.2
- these permutations begin with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' a... with $\mathrm{E}$ and end with $\mathrm{C}$ ? ====Solution==== The total number of letters in 'Excellence' a... with $\mathrm{E}$ and end with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' a... permutations do not begin with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' a
- Question 4 Exercise 6.4
- at is the probability of obtaining all heads? ====Solution==== First we construct a tree diagram to find out... at is the probability of obtaining two heads? ====Solution==== First we construct a tree diagram to find out... hat is the probability of obtaining one hcad? ====Solution==== First we construct a tree diagram to find out... e probability of obtaining at least one hcad? ====Solution==== First we construct a tree diagram to find out
- Question 1 Exercise 6.4
- e. What is the probability of rolling a $5$ ? ====Solution==== Rolling a $5$ Let \begin{align}A&=\{5\}\\ P(A... obability of rolling a number less than $1$ ? ====Solution==== Rolling a number less than $1$ Let \begin{ali... bility of rolling a number greater than $0$ ? ====Solution==== Rolling a number greater than $0$ Let \begin{... he probability of rolling a multiple of $3$ ? ====Solution==== Rolling a multiple of $3$ Let \begin{align}D&
- Question 3 & 4 Exercise 6.1
- dfrac{2}{7 !}+\dfrac{3}{8 !}=\dfrac{75}{8 !}$ ====Solution==== We are taking the L.H.S of the above given eq... ve that $\dfrac{(n+5) !}{(n+3) !}=n^2+9 n+20$ ====Solution==== We are taking the L.H.S of the above given eq... ac{n(n !)}{(n-5) !}=\dfrac{12(n !)}{(n-4) !}$ ====Solution==== We are given: \begin{align}\dfrac{n(n !)}{(n-... n !}{(n-4) !}: \dfrac{(n-1) !}{(n-4) !}=9: 1$ ====Solution==== We are given: \begin{align} \dfrac{n !}{(n-4)
- Question 12 Exercise 6.2
- WORM" if the letters are taken all at a time? ====Solution==== BOOKWORM\\ The total number of letters in wor... EPER" if the letters are taken all at a time? ====Solution==== BOOKKEEPER\\ The total number of letters in $... ABAD" if the letters are taken all at a time? ====Solution==== ABBOTABAD\\ Total number of letters are ten, ... TTER" if the letters are taken all at a time? ====Solution==== LETTER\\ The total number of letters in lette
- Question 9 Exercise 6.3
- mittee must contain four men and four women? ====Solution==== Total men are $7$ and total women are $6.$ T... be chosen if there must be at least two men? ====Solution==== Total men are $7$ and total women are $6$. T... e chosen if there must be at least two women? ====Solution==== Total men are $7$ and total women are $6.$ T... chosen if there must be more women than men? ====Solution==== Total men are $7$ and total women are $6$ Th
- Question 3 Exercise 6.4
- the probability that $8$ answers are correct. ====Solution==== We have $8$ questions, each question has two ... the probability that $7$ answers are correct. ====Solution==== We have $8$ questions, each question has two ... the probability that $6$ answers are correct. ====Solution==== We have $8$ questions, each question has two ... bility that at least $6$ answers are correct. ====Solution==== We have $8$ questions, each question has two
- Question 6 Exercise 6.4
- obability of each of the Drawing an ace card. ====Solution==== Total cards $$=52$$ An ace. Total ace cards $... f each of the Drawing either spade or hearıs. ====Solution==== Total cards $=52$ Drawing either space or he... bility of each of the Drawing a diamond card. ====Solution==== Total cards $=52$ Drawing a diamond card. T... obability of each of the Drawing a face card. ====Solution==== Total cards $=52$(iv) Drawing a face card. T
- Question 9 Exercise 6.5
- 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 })&=\... y that at least one of them will be selected. ====Solution==== \begin{align} P(\text { Ajmal scicction })&=\
- Question 7 & 8 Review Exercise 6
- )=0.5$ and $P(B / A)=0.4$, find $P(A \cap B)$ ====Solution==== We know that: \begin{align} P(B \mid A)&=\dfr... P(B)=0.5$ and $P(B / A)=0.4$, find $P(A / B)$ ====Solution==== We know that $$P(A \mid B)=\dfrac{P(A \cap B)... )=0.5$ and $P(B / A)=0.4$, find $P(A \cup B)$ ====Solution==== \begin{align} P(A \cup B)&=P(A)+P(B)-P(A \cap... ith $35$ and no-digits appear more than once? ====Solution==== If each telephone number starts with $35.$
- Question 3 and 4 Exercise 6.2
- nciple of counting $^n P_r=n(^{n-1} P_{r-1})$ ====Solution==== We are given that: $$^n P_r=n({ }^{n-1} P_{r-... 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({ }^{n-1}... partment arrange eight suspects in a line up? ====Solution==== The total number of suspects are eight sọ, $n
- Question 7 and 8 Exercise 6.2
- igits $1,2,3,4$ and 5 if repetitions allowed? ====Solution==== There are three places (hundred digit, ten di... ,2,3,4$ and 5 if repetitions are not allowed? ====Solution==== If repetition is not allowed then each digit ... n" if all the vowels are to be kept together? ====Solution==== The total number of alphabets in word equatio