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Consider a class of 5 girls and 7 boys. ...

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is

A

350

B

500

C

200

D

300

Text Solution

Verified by Experts

The correct Answer is:
D
Number of girls in the class = 5 and number of boys in the class = 7
Now, total ways of forming a team of 3 boys and 2 girls
`= ""^(7)C_(3) * ""^(5)C_(2) = 350`
But, if two specific boys are in team, then number of ways `= ""^(5)C_(1) * ""^(5)C_(2) = 50`
Required ways, i.e. the ways in which two specific boys are not in the same team = 350 - 50 = 300.
Alternate Method
Number of ways when A is selected and B is not
`= ""^(5)C_(2) * ""^(5)C_(2) = 100`
Number of ways when B is selected and A is not
`= ""^(5)C_(2) * ""^(5)C_(2) = 100`
Number of ways when both A and B are not selected `= ""^(5)C_(3) * ""^(5)C_(2) = 100`
`therefore` Required ways `= 100 + 100 + 100 = 300`.
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