A class consists of 16 students The instructor wants to pick

A class consists of 16 students. The instructor wants to pick a group of 4 to work on a special project. How many different groups of 4 can be choose?

Solution

No. of ways 4 can be selected from group of 16 = ¹⁶C₄

No. of ways 4 can be selected from group of 12 = ¹²C₄

No. of ways 4 can be selected from remaining 8 = ⁸C₄

No. of ways 4 can be selected from last 4 = ⁴C₄

So total no. of ways = ¹⁶C₄ * ¹²C₄ * ⁸C₄ * ⁴C₄
= 1820*495* 70*1 = 63063000

So 4groups are formed and order of selection of group is not important. So,

Total no. of ways = 63063000 ÷ 4! = 2627625