At a mall there are 5 jewelry stores. Allison is looking to purchase a necklace but only has time to visit 3 jewelry stores. In
how many paths could she take to visit 3 of the 5 stores at the mall?
Group of answer choices
10
20
60
125
2 answers:
Answer:
60
Step-by-step explanation:
I just took the quiz and I guessed 60. It was right
<u>Answer</u>:
she can take 60 different paths to visit 3 out of 5 stores.
<u>Step-by-step explanation:</u>
<u>Given</u>:
The number of jewelry shop in the mall=5
Number of shops allison can visit =3
<u>To Find</u>:
Number of ways in which Allison can visit the 3 among 5 shops=?
<u>Solution</u>:
we have to use permutations.
Here, 3 out of 5 stores has to be visited, then permutation is![5P_3 = \frac{5!}{(5-3)!}](https://tex.z-dn.net/?f=5P_3%20%3D%20%5Cfrac%7B5%21%7D%7B%285-3%29%21%7D)
= ![\frac{5!}{2!}](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B2%21%7D)
= ![\frac{(5\times4 \times3 \times2 \times1 )}{(2 \times1 )}](https://tex.z-dn.net/?f=%5Cfrac%7B%285%5Ctimes4%20%5Ctimes3%20%5Ctimes2%20%5Ctimes1%20%29%7D%7B%282%20%5Ctimes1%20%29%7D)
=![5 \times 4 \times 3](https://tex.z-dn.net/?f=5%20%5Ctimes%204%20%5Ctimes%203)
=![5\times 12](https://tex.z-dn.net/?f=5%5Ctimes%2012)
= 60
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