Permutation and Combination Aptitude Questions and Answers:

Answer: (b) 27

Solution: Any number between 100 and 1000 is of 3 digits. So, we can fill the unit place, tenth place, and hundred's place by all the three digits 3, 4, and 5, means each place by 3 ways.

Hence, the number of integers, $$ = 3 \times 3 \times 3 $$ $$ = 27 $$

Answer: (a) 4536

Solution: Any number between 1000 and 10000 is of four digits. Here, the numbers must have distinct digits. Here, repetition of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is not allowed and zero (0) cannot be filled on the extream left end.

Now, thousand's place can be filled by 9 ways.

hundredth place can be filled by 9 ways.

tenth place can be filled by 8 ways.

unit place can be filled by 7 ways.

Hence total four digit numbers,$$ = 9 \times 9 \times 8 \times 7 $$ $$ = 4536 $$

Answer: (b) 20

Solution: The first post can be filled in 5 ways, the second post can be filled in 4 ways.

Now, the total number of ways posts can be filled, $$ = 5 \times 4 $$ $$ = 20 \ Ways $$

Answer: (c) 480

Solution: Like the repetition of the digits is not allowed, and we have to form four digit odd numbers, so it is clear, that the unit place digit must be odd. So, we can fill the unit place by 1, 3, 5, and 7, that is in 4 ways.

Now, tenth digit can be filled by any of the remaining 6 numbers.

hundredth place can be filled by any of the remaining 5 numbers.

thousand's place can be filled by the remaining 4 numbers.

Hence, total number of ways,$$ = 4 \times 6 \times 5 \times 4 $$ $$ = 480 \ Ways $$

Answer: (d) 720

Solution: The first seat can be filled by 10 ways, second place can be filled by 9 ways, and third place can be filled by 8 ways.

Now, total number of ways, seats can be filled,$$ = 10 \times 9 \times 8 $$ $$ = 720 \ Ways $$

Answer: (a) 56

Solution: 3 sportsmen can be selected from the group of 8 by \(8C_3\) ways.

Hence, $$ 8C_3 = \frac{8!}{(8 - 3)! \times 3!} $$ $$ = \frac{8!}{5! \times 3!} $$ $$ = 56 \ Ways $$

Answer: (c) 48

Solution: Here, the repetition of the digits is allowed and we have to form three digit odd numbers, so it is clear that the unit place can be filled by 1, 3, and 5, that is in 3 ways.

Now, if the repetition of digits is allowed, so we can fill the tenth and hundredth place by any of the remaining four digits in 4 ways each.

Hence, $$ = 4 \times 4 \times 3 $$ $$ = 48 \ Ways $$

Answer: (a) 12

Solution: It can be arranged by, $$ = \frac{(5 - 1)!}{2} $$ $$ = \frac{4!}{2} $$ $$ = 12 \ Ways $$

Answer: (d) 7

Solution: Total number of flowers,$$ = 4 + 5 $$ $$ = 9 $$ Hence, total number of garlands, $$ = \frac{(9 - 1)!}{2} \times \frac{1}{4! \times 5!} $$ $$ = \frac{8!}{2 \times 4! \times 5!} $$ $$ = 7 \ Garlands $$

Answer: (c) 181,440

Solution: It can be arranged by,$$ = \frac{(10 - 1)!}{2} $$ $$ = \frac{9!}{2} $$ $$ = 181,440 \ Ways $$