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Question
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Solution
Given numbers are 1, 1, 2, 3, 3, 4
Here 1 occurs twice, 3 occurs twice.
∴ Number of distinct 6-digit numbers
= `(6!)/(2! xx 2!)`
= `(6 xx 5 xx 4 xx 3 xx 2!)/(2! xx 2 xx 1)`
=6 × 5 × 2 × 3
= 30 × 6
= 180
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