# Question 1 Review Exercise 6

Solutions of Question 1 of Review Exercise 6 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Chose the correct option.

i. In how many ways can we name the vertices of pentagon using any five of the letters $O, P, Q, R, S, T, U$ in any order?

• (a) $2520$
• (b) $9040$
• (c) $5140$
• (d) $4880$
(a): $2520$

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) $14$
• (b) $42$
• (c) $28$
• (d) $21$
©: $28$

iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ without repetition if the digits $3$ and $7$ must together?

• (a) $120$
• (b) $180$
• (c) $144$
• (d) $96$
(a): $120$

iv. Evaluate $\dfrac{(n+2) !(n-2) !}{(n+1) !(n-1) !}$

• (a) $(n-3)$
• (b) $(\dot{n}-1)$
• (c) $\dfrac{n+1}{n+2}$
• (d) $\dfrac{n+2}{n-1}$
(d): $\dfrac{n+2}{n-1}$

v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated?

• (a) $768$
• (b) $724$
• (c) $844$
• (d) $696$
(a): $768)$

vi. A committee of 4 people will be selected from 8 girls and 12 boys in a class. How many different selections are possible if at least one boy must be selected?

• (a) $2865$
• (b) $3755$
• (c) $4225$
• (d) $4775$
(d): $4775$

vii. The number of all possible matrices of order $3 \times 3$ with each entry 0 and 1 is:

• (a) $18$
• (b) $27$
• (c) $512$
• (d) $81$
©: $512$

viii. How many diagonals can be drawn in plane figure of 8 sides?

• (a) $21$
• (b) $20$
• (c) $35$
• (d) $81$
(b): $20$

ix. If $P(A)=\dfrac{1}{2}, P(B)=0$ then $P(A \mid B)$ is:

• (a) $0$
• (b) $\dfrac{1}{2}$
• (c) not defined
• (d) $1$
x. If $A$ and $B$ are events such that $P(A / B)=P(B / A)$ then
• (a) $A \subset B$ but $A \neq B$
• (b) $A=B$
• (c) $A \cap B=\phi$
• (d) $P(A)-P(B)$
(d): $A \cap B=\phi$