finding the number of possible groups of elements\njuan is making a fruit salad. he has grapes, watermelon…
finding the number of possible groups of elements\njuan is making a fruit salad. he has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. he wants his fruit salad to contain five different fruits. how many ways can he make the fruit salad if it must contain watermelon?\n21\n35\n56\n70
Answer
Explanation:
Step1: Determine remaining fruits to choose
Since watermelon is already in the salad, we need to choose 4 fruits from the remaining 7 fruits (grapes, apples, pineapple, bananas, mangoes, honeydew, cantaloupe).
Step2: Use combination formula
The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 7$ and $r=4$. $C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7!}{4!3!}=\frac{7\times6\times5\times4!}{4!\times3\times2\times1}=\frac{7\times6\times5}{3\times2\times1}=35$
Answer:
35