IIT JEE , AIEEE Forum - Mathematics , Algebra - a question of permutation and combination

vibhav1991

Ø Four dice are rolled once. Find the number of outcomes in which at least one die shows 3. explain.

answer-

671

sboosy

are they identical or not?please be more clear

priyesh

total outcomes of four die are 6 * 6 * 6 * 6 = 1296 (because 6 possibilities for each die)

no. of ways in which 3 does not occur in any of the four outcomes = 5 * 5 * 5 * 5 = 625 (because there are 5 possibilities for each die)

so no.of ways in which atleast one 3 occurs = total ways - no.of ways in which 3 does not occur = 1296 - 625 = 671 -----(ans)

roliesha

using binomial distribution,
prob. of 3 occuring exactly once = 1- 4C0 (5/6)^4 = (671/1296)
sample space = 6^4 = 1296
no. of favourable outcomes = (prob.) * (sample space)
= 1296 *( 671/ 1296)

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