Question

Twenty-four distinguishable balls are to be placed in six boxes.(DIFFERENT BOXES) (a) In how many different ways can this be done? (b) In how many different ways can this be done if box 1 must get 12 balls, box 2 must get 7 balls, box 3 must get 5 balls, and boxes 4, 5, and 6 must be empty?

Answer 1

Answer: a) 124,596, b) 2142691552.

Step-by-step explanation:

Since we have given that

Number of distinguishable balls = 24

Number of boxes = 6

(a) In how many different ways can this be done?

$^{24}C_6\\\\=134,596$

(b) In how many different ways can this be done if box 1 must get 12 balls, box 2 must get 7 balls, box 3 must get 5 balls, and boxes 4, 5, and 6 must be empty?

Number of ways would be

$\dfrac{24!}{12!7!5!}=2142691552$

Hence, a) 124,596, b) 2142691552.