Question 1 Review Exercise 6

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) $4880$
  See Answer

  (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) $21$
  See Answer

  ©: $28$

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) $96$
  See Answer

  (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) $\dfrac{n+2}{n-1}$
  See Answer

  (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) $696$
  See Answer

  (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) $4775$
  See Answer

  (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) $81$
  See Answer

  ©: $512$

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

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

  (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) $1$
  See Answer

  ©: not defined

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) $P(A)-P(B)$
  See Answer

  (d): $A \cap B=\phi$