Question

There are 7 singers competing at a talent show. In how many different orders can the singers appear?

Answer 1

7! = 7*6*5*4*3*2*1 = 5,040

Answer 2

There are 7 singers competing at the talent show. Thus, 7 singers can appear for the first place. Likewise, the remaining 6 singers can appear for the second place. In a similar fashion, 5 singers can appear for the third place. This will continue in this manner till the last place for which only 1 singer can appear. Therefore, the number of different orders in which the singers can appear is given as:

$7\times 6\times 5\times 4\times 3\times 2\times 1=7!=5040$

Therefore, out of the given options, second option is correct.