Question

Sara has six necklaces, but her mother will only allow her to wear two at a time. How many different combinations of two necklaces can Sara wear?

Answer 1

Answer:

15 different combinations

Step-by-step explanation:

Sara has six necklaces, but her mother will allow her to wear two at a time.

So we calculate different combinations of two necklaces by this formula:

$\frac{n!}{r!(n-r)!}$

Where n = 6 and r = 2

Now put the values

$\frac{6!}{2!(6-2)!}$

$\frac{6\times 5\times 4\times 3\times 2\times 1}{2!(6-2)!}$

$\frac{720}{2\times 1(4)!}$

$\frac{720}{2\times 1(4\times 3\times 2\times 1)}$

$\frac{720}{2(24)}$

$\frac{720}{48}$ = 15 combinations

Sara can wear 15 different combinations of two necklaces.

Answer 2

6C2 = (6 x5)/(2 x 1) = 15 difference combinations