Question

Simplify the expression 6C5. a.6. b. 24 C. 30 d. 720

Answer 1

Answer:  A) 6

=====================================================

Explanation:

Plug n = 6 and r = 5 into the nCr combination formula

$_n C _r = \frac{n!}{r!*(n-r)!}\\\\_6 C _5 = \frac{6!}{5!*(6-5)!}\\\\_6 C _5 = \frac{6!}{5!*1!}\\\\_6 C _5 = \frac{6*5*4*3*2*1}{5*4*3*2*1*1}\\\\_6 C _5 = \frac{720}{120}\\\\_6 C _5 = 6$

Or you could use the shortcut

$_n C _{n-1} = n$

Yet another path you could take is to use Pascal's Triangle. Locate the row that starts with 1,6,... and then locate the second to last item. That value in the triangle is 6.

A real world interpretation is to consider having 6 people and you are selecting 5 of them to form a group where order doesn't matter. How many ways are there to do this? Well there are 6 such ways because there are 6 ways to leave someone out of the group.