Question

How many different numbers of six digits can be formed from the digits 3,1,7,0,9,5 when repetition of digits is not allowed ?

Answer 1

We cannot have 0 at the first digit of six-digit numbers. Now, 5 digits are left including 0. So, second digit of six-digit numbers can be selected in 5 ways. Third digit of six-digit numbers can be selected in 4 ways. Fourth digit of six-digit numbers can be selected in 3 ways. Fifth digit of six-digit numbers can be selected n 2 ways. Last digit of six-digit numbers can be selected in 1 ways. Hence, total number of numbers = $5\times 5\times 4\times 3\times 2\times 1=600$