CAT 2022 Question Paper (Slot 1) Question 54

Question 54

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Correct Answer: 84


Let the number of balloons each child received be 2a, 2b, 2c and 2d

2a + 2b + 2c + 2d = 20

a + b + c + d = 10

Each of them should get more than zero balloons.

Therefore, total number of ways = $$(n-1)_{C_{r-1}}=(10-1)_{C_{4-1}}=9_{C_3}=84$$

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Nishita Bhajipale

1 month ago

How its sloved 9c3

Chaitanya Patil

3 months, 3 weeks ago

why to divide by 6? and how a1+b1+c1+d1= 6?

Thasni K S

2 months, 1 week ago

divide by 6 because it's 9C3 and 9-3 is 6.
a1+a2+a3+a4= (a+b+c+d)-(4*1) = 10-4 = 6. (add the terms a1+1 = a, b1+1=b......and solve for a1+b1+c1+d1)

Sukhdev Kumawat

2 months, 3 weeks ago

Nothing understood worst sir

Ganesh Kumar

4 months ago



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