Question

How many four digit different numbers, greater than 50000 can be formed with digits 1,5,9,0 when repetition is not allowed?

Answer 1

Assuming that each digit from 1,1,5,9,0 can be used only once, we put 5 or 9 for the leftmost (ten-thousands) position. Then we are left with either 1,1,9,0 or 1,1,5,0 for the remaining four positions. We can construct 4!/(1!×1!×2!)=12 distinct numbers with these digits, using the formula for repeated permutations. Multiplying this by 2gives the answer: 24