Out of 3 girls and 6 boys a group of three members is to be formed in such a way that at least one member is a girl. In how many different ways can it be done?
A) 64
B) 84
C) 56
D) 20
Answers
Answered by
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Case 1: 4 boys and 3 girls
Case 2: 5 boys and 2 girls
Case 3: 6 boys and 1 girl
Case 1 combinations:
Select 4 boys out of 6 (6C4 ways)
Select 3 girls out of 4 (4C3 ways)
Total ways = 6C4 * 4C3 = 60 ways
Case 2 combinations:
Select 5 boys out of 6 (6C5 ways)
Select 2 girls out of 4 (4C2 ways)
Total ways = 6C5 * 4C2 = 36 ways
Case 3 combinations:
Select 6 boys out of 6 (1 way)
Select 1 girl out of 4 (4C1 ways)
Total ways = 1 * 4C1 = 4 ways
Total possible combinations = 60 + 36 + 4 = 100 ways
Case 2: 5 boys and 2 girls
Case 3: 6 boys and 1 girl
Case 1 combinations:
Select 4 boys out of 6 (6C4 ways)
Select 3 girls out of 4 (4C3 ways)
Total ways = 6C4 * 4C3 = 60 ways
Case 2 combinations:
Select 5 boys out of 6 (6C5 ways)
Select 2 girls out of 4 (4C2 ways)
Total ways = 6C5 * 4C2 = 36 ways
Case 3 combinations:
Select 6 boys out of 6 (1 way)
Select 1 girl out of 4 (4C1 ways)
Total ways = 1 * 4C1 = 4 ways
Total possible combinations = 60 + 36 + 4 = 100 ways
Answered by
0
I think it is in 84 ways .
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