Example 7: Calculate

₃ C <sub>2

5</sub> C ₅

Solution:

₃ C ₂ = 3! / [ (3 - 2)!2! ] = 6 / [1 * 2] = 3 (problem of points and lines solved above in example 6)

₅ C ₅ = 5! / [(5 - 5)!5! ] = 5! / [0!5!] = 5! / [1 * 5!] = 1 (there is only one way to select (without order) 5 items from 5 items and to select all of them once!)

Example 8:We need to form a 5 a side team in a class of 12 students. How many different teams can be formed?

Solution:

There is nothing that indicates that the order in which the team members are selected is imoportant and therefore it is a combination problem. Hence the number of teams is given by

₁₂ C ₅ = 12! / [ (12 - 5)!5! ] = 792

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