Answer :

5C1 + 5C2 + 5C3 + 5C4 + 5C5


= 5C1 + 5C2 + 5C2 + 5C1 + 5C5 (5C1 = 5C4 and 5C2 = 5C3)


= 2 5C1 + 2 5C2 + 5C5


= 2 5 + 2 + 1


= 10 + 20 + 1


= 31

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