the number of ways of selecting a team of 3 boys and 2 girls from 6 boys & 4 girl is
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Answer:
For the first combination of boys as X’s and x’s, the girls options are as O’s and o’s. Bold, capitol X’s and O’s represent selected boys and girls.
X X X x x x O O o o o
X X X x x x O o O o o
X X X x x x O o o O o
X X X x x x O o o o O
X X X x x x o O O o o
X X X x x x o O o O o
X X X x x x o O o o O
X X X x x x o o O O o
X X X x x x o o O o O
X X X x x x o o o O O
10 ways to pic 2 girls out of 5 girls above.
Now we repeat the sequence of selected girls represented by O’s and o’s, above, for each of the 19 remaining possible combinations of the boys shown by X’s and x’s below.
X X x X x x
X X x x X x
X X x x x X
X x X X x x
X x X x X x
X x X x x X
X x x X X x
X x x X x X
X x x x X X
x X X X x x
x X X x X x
x X X x x X
x X x X X x
x X x X x X
x X x x X X
x x X X X x
x x X X x X
x x X x X X
x x x X X X
20 variations of 3 of 6 boys above.
There are 4 + 3 + 2 + 1 = 10 ways to choose 2 girls out of 5 girls for every:
10 + 6 + 3 + 1 = 20 ways to choose 3 boys out of six boys.
10 * 20 = 200 ways to pick 3 boys and 2 girls out of a pool of 6 boys and 5 girls.
Answer:
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