How many different ways can a party of seven politicians be

How many different ways can a party of seven politicians be seated in a row? How many different three-digit numbers can be formed from the digits 1, 2, 3, 7, 8, 9, without reusing the digits?

Solution

(1) Number of politicians = 7

Since, first position in row can be fill in 7 ways, then second position of row can be fill in 6 ways, third position can be fill in 5 ways,....., and so on last position of row can be fill in 1 ways.

Total number of different ways = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

(2) We have 6 digits 1, 2, 3, 7, 8 and 9.

To fill ones place, numbers of ways = 6

since digits can not be repeated, so number of ways to fill tens position = 5

number of ways to fill hundred position = 4

Total number of ways = 6 * 5 * 4 = 120

hundred digit (4 ways)

tens digit ( 5 ways )

onesdigit ( 6 ways)