You have 6 bracelets and 15 necklaces. Find the number of ways you can wear one bracelet and one necklace.
Mathematics · High School · Tue Nov 03 2020
Answered on
Given:
You have 6 bracelets and 15 necklaces.
Determine the number of ways to wear one bracelet and one neclace.
Solution:
The number of ways can be determined by using the combination formula denoted as,
nCr = n!/r! (n-r)!
15C6 = 15! / 6! (15 - 6)!
15C6 = 15! / 6! 9!
15C6 = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1/ 6 x 5 x 4 x 3 x 2 x 1 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 or 9! cancels leaving behind
15C6 = 15 x 14 x 13 x 12x 10 / 6 x 5 x 4 x 3 x 2 x 1
15C6 = 5,005
Final answer:
There are 5,005 way to wear one bracelet and one neclace.