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you have five fruits and you want to choose three of them to combine into a fruit smoothie. in how many ways can three fruits be selected from the five fruits that you have? A.1 B.10 C.5 D.60

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dakodikg
You have five fruits and you want to choose three of them to combine into a fruit smoothie. In how many ways can three fruits be selected from the five fruits that you have?
B.10 is the answer

I know it's a multiple choice and all you really need it the letter that is the answer, but let me know if you want an explanation

Answer:  The correct option is (B). 10.

Step-by-step explanation:  Given that there are five fruits and we want to choose three of them to combine into a fruit smoothie.

We are to find the number of ways in which three fruits be selected from the five fruits.

We will be using the following combination formula for n elements choosing r (r is less than or equal to n) at a time:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]

Here, n = 5  and r = 3.

Therefore, the required number of ways is given by

[tex]^5C_3\\\\\\\dfrac{5!}{3!(5-3)!}\\\\\\=\dfrac{5!}{3!2!}\\\\\\=\dfrac{5\times 4\times 3!}{3!\times 2\times 1}\\\\\\=5\times 2\\\\=10.[/tex]

Thus, the required number of ways is 10.

Option (B) is CORRECT.

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