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In how many ways 9 balloons can be divided into 3 groups such that a team contains 3 balloons in each team.

Option: 1

84


Option: 2

280


Option: 3

30


Option: 4

250


Answers (1)

best_answer

The given information is:

Number of balloons =9

Number of groups =3

Number of balloons in each groups =3

Pick first 3 balloons from 9 balloons, 

Total no. of ways of choosing is:

\frac{9 !}{(9-3) ! 3 !}=\frac{9 !}{6 ! 3 !}=84

Pick next 3 balloons from 6 balloons,

Total no. of ways of choosing is:

\frac{6 !}{(6-3) ! 3 !}=\frac{6 !}{3 ! 3 !}=20

Pick last 3 balloons from remaining 3 balloons and the number of ways this can be done is 1 .

Since the three groups are similar, there is no differentiation between them. Therefore, we need to divide it with 3 !=6 .

The total numbers of ways:

\frac{84 \times 20}{6}=280

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manish

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