Combinations - how to show that 10C2=10C8

The most effective way to show that 10C2 = 10C8 is to solve for the values of each combination. To solve for the values, we have to make use of the combination formula:

nCr = n! / r! (n - r) !

where n is the total sample size and r is the selected sample size

Calculating the value of 10C2:

10C2 = 10! / [2! (10 - 2) !]

10C2 = 10! / (2! * 8!)

10C2 = 45

Calculating the value of 10C8:

10C8 = 10! / [8! (10 - 8) !]

10C8 = 10! / (8! * 2!)

10C8 = 45

Therefore,

10C2 = 10C8