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  • How many ways 15 people can be divided into 3 groups, such that all three of them contain 5 people each.Option: 1 <img alt="128128" src="ht

How many ways 15 people can be divided into 3 groups, such that all three of them contain 5 people each.

Option: 1

128128


Option: 2

128


Option: 3

126126


Option: 4

126


Answers (1)

best_answer

Number of people =15

Number of groups =3
Number of people in all groups =5
Pick first 5 people from 15 people, Total no. of ways of choosing is:
\frac{15 !}{(15-5) ! 5 !}=\frac{15 !}{10 ! 5 !}=3003
Pick next 5 people from 10 people, Total no. of ways of choosing is:
\frac{10 !}{(10-5) ! 5 !}=\frac{10 !}{5 ! 5 !}=252

Pick last 5 people from 5 people 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{3003 \times 252}{6}=126126

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Gunjita

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