Question

Barbara has 7 swimsuits. She needs to take 4 swimsuits on a vacation. In how many different ways can she choose 4 swimsuits out of 7
A. 35
B. 840
C. 24
D. 210

Answer 1

You should use here the formula for combinations

$C_n^k=\dfrac{n!}{k!(n-k)!}.$

In your case n=7, k=4, then

$C_7^4=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!\cdot 3!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{4!\cdot 2\cdot 3}=5\cdot 7=35.$

Answer: 35 ways, option A.