probability

Question

a dice is tossed seven times what is the probability that all six faces appear at least once?

a)63/64

b)35/648

c)2/9

d)5/324

Answer 1

Total Number of combinations possible at 7 places = 6⁷

Out of 6 numbers, 1 will repeat.

Thus, a number can be chosen in 6 ways and it will appear at 2 positions which can be chosen in ⁷C₂ ways.

Rest of the 5 places (2 filled by a number) can be filled in 5! ways.

Thus probability = ( 6 * ⁷C₂ * 5! ) / (6⁷)

 Answer is B