How many kinds of integers can be made by arranging three cards among six cards of 1, 2, 2, 3, 4, 5?
Answer
72
Solution
① In case card of 2 is not use
Answer
72
Solution
① In case card of 2 is not use
4 × 3 × 2 = 24 integers can be made.
② In case one card of 2 is used
There are three patterns of 2XY, X2Y, ans XY2 and are 4 × 3 = 12 kinds of arranging cards respectively.
Thus there are 12 × 3 = 36 integers can be made.
③ In case two cards of 2 are used
There are three patterns of 22X, 2X2 and X22 and there are 4 kinds of arranging cards respectively.
Thus there are 4 × 3 = 12 integers.
Therefore, there are 24 + 36 + 12 = 72 integers in all.
