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Lina20 [59]
3 years ago
9

Luis is packing his bags for his vacation he has 9 unique toy animals but only 5 fit in his bag how many different groups of 5 t

oy animals can he make
Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

Answer:

126 groups

Step-by-step explanation:

we know that

This is a combination problem, because the order doesn't matter.  He has 9 toys and wants to know the number of different combinations of 5 he can take.

The formula for the number of possible combinations of r objects from a set of n objects is given by

^nC_r=\frac{ {n!}}{r!(n-r)!}

In this problem we have

n=9, r=5

substitute

^9C_5=\frac{ {9!}}{5!(9-5)!}

^9C_5=\frac{ {9!}}{5!(4)!}

^9C_5=\frac{ {(9)(8)(7)(6)5!}}{5!(4)!}

^9C_5=\frac{ {9)(8)(7)(6)}}{(4*3*2*1)}

^9C_5=126

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