juan is making a fruit salad. he has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and…
juan 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?\no 21\no 35\no 56\no 70
Answer
Answer:
B. 35
Explanation:
Step1: Determine remaining fruits
Since watermelon is fixed, there are 7 remaining fruits and we need to choose 4.
Step2: Use combination formula
The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 7$ and $r=4$.
Step3: Calculate factorial values
$n!=7!=7\times6\times5\times4\times3\times2\times1$, $r!=4!=4\times3\times2\times1$, $(n - r)!=(7 - 4)!=3!=3\times2\times1$.
Step4: Substitute values
$C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7\times6\times5\times4!}{4!\times3!}=\frac{7\times6\times5}{3\times2\times1}$.
Step5: Simplify
$\frac{7\times6\times5}{3\times2\times1}=35$.