Question

What is the number of unique possible screen names if Gaga wants to use the arrangement of her first name followed by arrangements of the year of her birth 1986?

Answer 1

Number of unique possible screen names `=144`

Explanation:

This is a problem about permutation

For GAGA, there are 4 letters in the name 2 As and 2 Gs

number of permutation `=(n!)/(n_1 !*n_2 !)=(4 !)/(2 !* 2 !)=6`

For the number 1986, there are 4 digits all unique from each other

4 digits taking 4 at a time, we have

number of permutation `=(n !)/((n-r) !)=(4 !)/((4-4) !)=24`

Number of unique possible screen names `=6*24=144`

God bless....I hope the explanation is useful.