The total combination will be, 45195 if the selecting dance troupe with 6 girls and 7 boys out of 20 girls and 15 boys who auditioned.
A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Selecting a dance troupe with 6 girls and 7 boys out of 20 girls and 15 boys who auditioned.
It is a combination problem:
Selecting 6 girls out of 20 = C (20, 6)
Selecting 7 boys out of 15 = C (15, 7)
Total combination = C (20, 6) + C (15, 7)
= 38760 + 6435
= 45195
Thus, the total combination will be, 45195 if the selecting dance troupe with 6 girls and 7 boys out of 20 girls and 15 boys who auditioned.
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