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- Question 7 Exercise 6.4
- . Find the probability of getting doublet of even numbers. ====Solution==== The sample space rolling a pai... 5) & (6,6) \end{array}\right]\end{align} So total number of sample points are $$n(S)=6 \times 6=36$$ doublet of even numbers. Let \begin{align}A&=\{(2,2),(4,4),(6,6)\}\\ n(... nce the possibility of getting doublet of an even number is: $$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{36}=\dfra
- Question 9 Exercise 6.3
- re $7$ and total women are $6.$ Therefore, Total number of persons $=7+6=13$ Committee consist of 8 pers... e contain exactly four men and four women. Total number of different ways that four men to be selected are: ${ }^7 C_4$. Total number of different ways that four women to be selected ... . By fundamental principle of counting the total number of different committees that will exactly contain
- Question 13 Exercise 6.2
- war, Pakistan. =====Question 13(i)===== Find the number of permutation of word "Excellence." How many of ... in with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' are: $n=10$, out of wh... 2$ are $C$. Therefore, \begin{align}\text{total number of permutations are} &=\left(\begin{array}{c} n ... d $m_3=2$ are $C$. Therefore, \begin{align}\text{Number of permulations are} &=\left(\begin{array}{c} n \
- Question 7 and 8 Exercise 6.2
- n. =====Question 7(i)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if... us by fundamental principle of counting the total number of three digits in this case are: $$m_1 \cdot m_2... =====Question 7(ii)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if... t allowed then each digit can appear once in each number. In this case $E_1$ occurs in $m_1=5$ different
- Question 11 Exercise 6.2
- shawar, Pakistan. =====Question 11===== How many numbers each lying between $10$ and $1000$ can be formed... 9$ using only once? ====Solution==== We will form numbers greater than $10$ and less than $1000$. So some number will consist just two digits, and some will conta... e digits. Thus we split into two parts as:\\ (i) Numbers greater than $10$ but less than $100$ These num
- Question 9 & 10 Review Exercise 6
- eshawar, Pakistan. =====Question 9===== How many numbers greater than a million can be formed with the di... on $=100,0000$. First we are computing the total number of ways arranging these digits using repeated per... {3 ! \cdot 2 !}=420 $$ But we have find the total number that are greater than $1$ million. In this case number should not start with $0$, therefore the total
- Question 5 and 6 Exercise 6.2
- 'Fasting' be arranged? ====Solution==== The total number of alphabets in 'Fasting' are $7.$ Thus the total number of possible arrangements to fill $7$ places by th... align} =====Question 6===== How many four digits number can be formed from the digits $2,4,5,7,9$ ? (Repe... tation as: $$^5 P_4=\dfrac{5 !}{5-4} !=120$$ Even Numbers Out of these for even number, the unit digit h
- Question 9 Exercise 6.2
- e given by six flags of different colors when any number of them used at a time? ====Solution==== We have ... . If each signal consist of one color then total number of signals $=^6 P_1=6$. If each signal consist of two color then total number of signal $s=^6 P_2=30$. If each signal consist of three color then total number of signals $=^6 P_3=120$. If each signal consist
- Question 10 Exercise 6.2
- itting next to each other? ====Solution==== Total number of seats are eight, so $n=8$. Number of students are five so, $r=5$. The total number of ways these five students can be seated are: \begin{a... will be considered as 7. In this case the total number of ways are: \begin{align}^2 P_2 \times^7 P_4&=2
- Question 12 Exercise 6.2
- at a time? ====Solution==== BOOKWORM\\ The total number of letters in word BOOKWORM are $8.$ $n=8$ out o... hree are $\mathrm{O}$, so $m_1=3$.. Thus total number of different words using all at a time are: \begi... t a time? ====Solution==== BOOKKEEPER\\ The total number of letters in $\mathrm{BOOK}$ KEEPER are ten. $n... wo are $\mathrm{K}$, so $m_3=2$. Thus the total number of different words are: \begin{align} \left(\begi
- Question 10 Exercise 6.5
- apples or both are good? ====Solution===== Total number of Apples $=20$ number of Oranges $=10$ number of defective apples $=5$ number of defective oranges $=3$. Totál good apples $=15$ Defective apples $=
- Question 1 Exercise 6.4
- ling a dice. What is the probability of rolling a number less than $1$ ? ====Solution==== Rolling a number less than $1$ Let \begin{align}B&=\{\}\\ &=\phi \text{t... ling a dice. What is the probability of rolling a number greater than $0$ ? ====Solution==== Rolling a number greater than $0$ Let \begin{align}C&=\{1,2,3,4,5,6\}
- Question 2 Exercise 6.4
- bility that all are green? ====Solution==== Total number of balls are: $4+5+6=15$ balls Total number of ways drawing three balls at random are: $${ }^{15} C_3=\d... !}{(15-3) ! 3 !}=455 $$ All are green The total number ways of favorable outcomes for green balls are: $... bility that all are white? ====Solution==== Total number of balls are: $4+5+6=15$ balls Total number of w
- Question 5 Exercise 6.4
- of $3$ men and $2$ women. ====Solution==== Total number of persons $=6+4=10$. Total number of ways to select $5$ out of these $10$ are: \begin{align}{ }^{10)} C_... $2$ women. By multiplication principle the total number of ways, selecting $3$ men and $2$ worncn are: \b... of $2$ men and $3$ women. ====Solution==== Total number of persons $=6+4=10$. Total number of ways to sel
- Question 3 and 4 Exercise 6.5
- =====Question 4===== A bag contains $30$ tickets numbered from $1$ to $30.$ One ticket is selected at random. Find the probability that its number is either odd or the square of an integer. ====Solution==== Total numbers written on tickets are \begin{align}S&=\{1,2,3, ... \ n(S)&=50 \end{align} Let \begin{align}A \{odd \,numbers \}&=\{1,3,5,..,29\}\\ n(A)&=15\\ \text{Let}\, B&