a die is rolled ten times.find the number of ways so that outcomes always contain 1,2,3.

please explain solution as well..

Dear Kunal,

the number of times the number 1,2,3 appear when the dice is rolled once is 1/3

so number of times it is possible to get 1,2,3 when dice is rolled 10 times is 1/3^ 10

1/59049 = 0.000016935

it is raised to the power 10 because when 10 dice rolled, the number or possibilities = 6^10 = 60466176
and the number of possibilities of getting 1,2,3 are 103 approximately.

approve if you are pleased with the answer

total no. of possibilities=6^10

You have got 10 places,

choose any 3 places by 10 C 3 ways=120 and fix 1 2 & 3 there...

7 places are left, they can have any of numbers, your conditions will be satisfied.

so the ANSWER is 120*(6^7)