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11. Combinations and Permutations Example 5:


Fred has a voucher to pick any two of the top 10 PS4 games! How many different combinations of 2 games can he pick?


10


C = × × ==


2


10 9 21


90 2 45


PROJECT 11.1 Games – Permutations


The top ten PS4 games are called: A, B, C, D, E, F, G, H, I, J. Write down all the possible ways in which Fred can pick two of them! If Example 6 is correct it should be 45.


Example 6:


From 10 games, how many ways can: 0 games be picked =


10 C 1= 0


1 game be picked = 2 games be picked = 3 games be picked = 4 games be picked = 5 games be picked = 6 games be picked = 7 games be picked = 8 games be picked = 9 games be picked = 10 games be picked =


10


10 C 1


10 2 1==1


10 9 21


10


C = × × ==


10


C = ×× ×× =


3 10 4


90 2 45


10 9 8 32 1 120


C = ×× × ×× × =


10 9 8 7 43 2


10 5 ××3 1 210


10 9 8 7 6 C 54= × ×××


10 C6 10 7 3 32 1 252×× =


= × ××× × ×× × ×


10 9 8 7 6 5 65 4


2× =


10 98 7 6 54 C 7 6 54 32 1 120


= × ××× × × ××× × ×


10 8 × =


C 10= × ××× × × × ×× × × × × × =


98 7 6 54 3 87 6 5 4 3 2 C9 1 45


10 = ××10 9 87 6 5 4 3 2 8


10 C10 = × 9


98 7 6 54 32 1 10 ×× × × × ×


10 98 7 6 54 32 1 1 ××× × × × × ×


××× × × × × × = 10 98 7 6 54 32 1


× ××× × × × × × = 107 1 210


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