Question

Q30 Calculate the number of ways in which 12 distinct candies can be divided among 2 children in a way that the first child gets 5 ca
candies.
88
Ops: А.
o 1,584
70836-
B.
O 3,792
C.
O 27,720
D.
13,860​

Answer 1

Step-by-step explanation:

B

Answer 2

Given: 12 distinct candies can be divided among 2 children in a way that the first child gets 5 candies.

To find: Total number of ways

Explanation: The total number of candies= 12

The first child gets 5 candies. Then the second child gets (12-5) = 7 candies

Therefore, out of these 12 candies we choose 7 candies.

Total number of ways to choose r candies out of n candies is:

$\binom{n}{r}$

Using this formula:

$\binom{12}{7}$

= 12! / 7! × 5!

= 12 ×11×10×9×8×7! / 7! × 5!

= 12 ×11×10×9×8/ 5×4×3×2×1

= 792 ways

Now, these 7 candies can be given to any of the two children(can be arranged in 2! ways). Therefore, the result should be multiplied by 2! for getting the total number of ways.

Total number of ways of distribution

= 792 × 2!

= 792 × 2×1

= 1584

Therefore, the total number of ways of distributing 12 candies such that the first one gets 5 candies is option (a) 1584.