Question

You have received 16 different gifts from the HR. You need to distribute it amongst 3
individuals. The first person must get 4 gifts, the second person must receive 8 gifts
and the third person must receive 4 gifts. What are the total number of ways to
achieve this?​

Answer 1

Given :   You have received 16 different gifts from the HR.

You need to distribute it amongst 3 individuals.

The first person must get 4 gifts,

the second person must receive 8 gifts

and the third person must receive 4 gifts.

To Find :  the total number of ways to achieve this

Solution:

For first person gifts can be selected in  ¹⁶C₄  ways

for second person 8 gifts out of remaining 12 gifts can be selected in   ¹²C₈ ways

for third person 4 gifts out of remaining 4 gifts can be selected in 1 way only    ⁴C₄  

Hence total Ways =  

¹⁶C₄* ¹²C₈ * ⁴C₄   =   9,00,900

total number of ways to distribute gifts = 900900

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