- #1
Michael_Light
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Homework Statement
I have 6 cards with the digits 1,2,2,3,4 and 5 written on each of them. In how many ways can I arrange 3 out of the 6 cards in a row?
Homework Equations
The Attempt at a Solution
Case 1: Only one card with digit '2' two is taken, so 5P3 =60
Case 2: Both cards with digit '2' are used. So 4 x (3!/2) =12
Total: 60+12 =72
My question is, do we need to consider the third case where no cards with digit '2' is taken, which gives additional arrangement of 4! =24?
I really confused.. Please guide me.. Or do we have other method to solve this..? Thanks..