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Home Q & A Board Science-Related Homework Help Mathematics
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fosmanali01 fosmanali01
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10 years ago
From a group of 4 adults and 3 children, 3 people are to be selected to sing together. If, at most, 2 adults can be selected, the total number of ways the group can be chosen can be calculated by using.

a. 7C3 - 4C3

b. 4C2 x 3C1

c. 3C1 x 6C2

d. 6C3

This is what I got:

Case 1: 7C3

Case 2: 4C2

7C3 x 4C2 = 210

Thank you for helping
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#1
Donated
Valued Member
10 years ago
Answer: A 7C3 - 4C3 = 35 - 4 = 31
7C3 = all possibilities
4C3 = The combinations where 3 adults were the 3 singers.
Remove the combinations where 3 adults were the 3 singers from all of the possibilities, and you get the combinations with 2 or less adults: 7C3 - 4C3

Possible scenarios:
All the children:
Child1, Child2, Child3 = 1
Two children, one adult:
Child1, Child2 * 4C1 = 4
Child1, Child3 * 4C1 = 4
Child2, Child3 * 4C1 = 4
One adult, Two children:
Child1 * 4C2 = 6
Child2 * 4C2 = 6
Child3 * 4C2 = 6
Sum of 31 possibilities.

A 7C3 - 4C3 = 35 - 4 = 31
b. 4C2 x 3C1 = 6 * 3 = 18
c. 3C1 x 6C2 = 3 * 15 = 45
d. 6C3 = 40
Pretty fly for a SciGuy
wrote...
#2
10 years ago
Good info on this site..
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