Permutation and combination

Answer 1 : A three digit number is to be formed . Therefore the first digit can be arranged in 4p1 ways and the remaining 2 digits can be arranged in 5p2ways . Hence the number of numbers that can be formed with the digits 0,2,3,4,5 is 4p1 * 5p2 = 4*5*4 = 80 . The number of numbers that are odd are 5p2 * 2p1 = 5*4*2 = 40 

Answer 2 : When no digits are repeated  - 

                The number of numbers of 5 digits which are odd that can be formed with the digits 0,1,2,3,4 are  

3p1 * 3p3 * 2p1 = 3*3*2*1*2 = 36

Ok ...

1. a.)The first digit can be choosen in 4 ways(excluding 0). now the second and third digit can be choosen in 5 ways so answer is 4*5*5 = 100

b.) The first digit can be choosen in 4 ways, the second digit in 5 ways and third digit in 2 ways(only 3,5) hence answer is 4*5*2 =40.

2. the odd number in the units place can be selected in 2 ways now  0 can be placed in the middle 3 places in 3 ways. the rest of numbers can be arranged in 3! ways so answer is 2*3*6 =18