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- Question 13 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... , Pakistan. =====Question 13(i)===== Find the number of permutation of word "Excellence." How many of these permutations begin with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' are: $n=10$, out of w
- Question 9 Exercise 6.3
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... Question 9(i)===== An $8$-persons committee is to be formed from a group of $6$ women and $7$ men. In how many ways can the committee be chosen if (i) committee must contain four men and... $7$ and total women are $6.$ Therefore, Total number of persons $=7+6=13$ Committee consist of 8 per
- Question 7 Exercise 6.4
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... ind the probability of getting doublet of even numbers. ====Solution==== The sample space rolling a pair of dice is \begin{align}S&=\{(i, j) ; i, j=1,2,3,4,5,6\}\\ &=\left[\begin{array}{llllll} (1,1) & (1,2) & (1,3) & (1,4) &
- Question 7 and 8 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... =====Question 7(i)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if repetitions allowed? ====Solution==== There are th... hundred digit, ten digit and unit digit place) to be filled by five digits, Moreover repetition is a
- Question 12 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... ==Question 12(i)===== How many different word can be formed from the letters "BOOKWORM" if the letters... a time? ====Solution==== BOOKWORM\\ The total number of letters in word BOOKWORM are $8.$ $n=8$ out ... e are $\mathrm{O}$, so $m_1=3$.. Thus total number of different words using all at a time are: \beg
- Question 9 Exercise 6.5
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... $2$ vacancies. The probability of their selection being $\dfrac{1}{7}$ and $\dfrac{1}{5}$ respectively. Find the probability that both will be selected. ====Solution==== \begin{align} P(\text { Ajmal scicction })&=\dfrac{1}{7} \\ \Rightarrow P(
- Question 10 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... ion 10(i)===== In how many ways can five students be seated in a row of eight seals if a certain two s... ing 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 thes
- Question 5 and 6 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... In how many ways can letter of the word 'Fasting' be arranged? ====Solution==== The total number of alphabets in 'Fasting' are $7.$ Thus the total number of possible arrangements to fill $7$ place
- Question 1 Exercise 6.4
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... =====Question 1(a)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... lling a $5$ ? ====Solution==== Rolling a $5$ Let \begin{align}A&=\{5\}\\ P(A)&=\dfrac{n(A)}{n(S)}\\ &=... =====Question 1(b)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p
- Question 9 & 10 Review Exercise 6
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9===== How many numbers greater than a million can be formed with the digits $2,3,0,3,4,2,3$? ====Solution==== We know that... $=100,0000$. First we are computing the total number of ways arranging these digits using repeated pe
- Question 11 Exercise 6.2
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... war, Pakistan. =====Question 11===== How many numbers each lying between $10$ and $1000$ can be formed with digits $2.3,4,0,8,9$ using only once? ====Solution==== We wil
- Question 10 Exercise 6.5
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... ples 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 app
- Question 5 Exercise 6.4
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... stion 5(i)===== A committee of five persons is to be selected at random form $6$ men and $4$ women. Fi... $3$ 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
- Question 3 and 4 Exercise 6.5
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... exclusive, therefore $A \cap B=\emptyset$. Thus \begin{align}P(A \cup B)&=P(A)+P(B)\\ \Rightarrow P(B... ===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. ====S
- Question 1 Review Exercise 6
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... $2520$</collapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if repeated digits are allowed? * %%(a)%% $14... c): $28$ </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}