A class consists of 3 boys and 6 girls willing

glycleWogry

glycleWogry

Answered question

2022-06-14

A class consists of 3 boys and 6 girls willing to form 3 groups of 3 called Groups A, B, C.
How many ways are there to assign them to the groups such that exactly 1 group has no boys?

Answer & Explanation

lodosr

lodosr

Beginner2022-06-15Added 24 answers

The label of the no boy group can be chosen in 3 ways. For each such way, the girls who will be in that group can be chosen in ( 6 3 ) ways.
Now consider the group lowest in the alphabet which will have at least one boy. That group can have (1) 1 boy or (ii) 2 boys.
To count (i), the boy can be chosen in ( 3 1 )
ways, and for each choice of boy the 2 girls can be chosen in ( 3 2 ) ways, for a total of ( 3 1 ) ( 3 2 ) .
The same argument shows that the count of (ii) is ( 3 2 ) ( 3 1 ) .
That gives a total of 18. Multiply by 3 ( 6 3 ) .
Because there are many ways to count, we do the arithmetic. The total number of ways is (3)(20)(18), which is 1080.

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