A house painter removed the brass numerals indicating the ho

A house painter removed the brass numerals indicating the house number from the door of 72712 Main Street. Later, the painter forgot the house number and tried to recall it by rearranging the five brass numerals. How many different house numbers can be formed by rearranging the five numerals 7, 2, 7, 1, and 2?

Solution

There are 5 numbers ( we assume here without repitition)

and 7 is repeated twice

Since he forgot he tries all possibilities

I number can be selected in 5 ways, ii in 4, iii in 3, iv in 2 and v in 1

Hence total different numbers that can be formed = 5(4)(3)(2)(1)/2! (since 7 is repeated twice)

= 60