A die is rolled 12 times Given that two of the rolls came up

A die is rolled 12 times. Given that two of the rolls came up 1, four came up 2, three came up 3, one came up 4, two came up 5, and none came up 6, how many different arrangements of the outcomes are there?

Solution

Outcomes , 1 1 2 2 2 2 3 3 3 4 5 5

No. of arrangements = 12! / (2!*4!*3!*2!) = 831600 Answer