How many arrangements of five letters from the word 'certain' contain the letter 't'? Explain your reasoning.

Answer 1

All possible cases = 7x6x5x4x3 = 2520
cases without the t = 6x5x4x3x2 = 720

so cases that contain the t = 2520 - 720 = 1800

OR

One spot taken by the t, leaves 4 others to fill
= 6x5x4x3 = 360

but the t could be in 5 different places
so total number with a t = 5x360 = 1800