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Solution


Q.

The number of ways of getting a sum 16 on throwing a dice four times is ______.                 [2024]

Ans.

(125)

We need sum of 16 on throwing a dice four times so possible ways are:
{(4, 4, 4, 4), (5, 4, 4, 3), (5, 5, 1, 5), (5, 5, 3, 3), (5, 5, 4, 2), (6, 4, 3, 3), (6, 4, 4, 2), (6, 5, 3, 2), (6, 5, 4, 1), (6, 6, 3, 1), (6, 6, 2, 2)}

Obtained Result Number of Ways
(6, 6, 2, 2) 4!2!2!=6
(6, 6, 3, 1) 4!2!=12
(6, 5, 4, 1) 4!=24
(6, 5, 3, 2) 4!=24
(6, 4, 4, 2) 4!2!=12
(6, 4, 3, 3) 4!2!=12
(5, 5, 4, 2) 4!2!=12
(5, 5, 3, 3) 4!2!2!=6
(5, 5, 1, 5) 4!3!=4
(5, 4, 4, 3) 4!2!=12
(4, 4, 4, 4) 1!=1
Total ways 125