Question

Marco needs to make a five letter password, without repeating any letters. How many different passwords could Marco make?
A.) 120
B.) 5,640,000
C.) 7,893,600
D.) 11,881,376

Answer 1

Answer:

7,893,600

Step-by-step explanation:

Permutations

n = possible things used (26 letters)

r = how many at a time (5 at a time - this is without repeating)

nPr = n! / (n - r)!

26P5 = 26! / (26 - 5)!

26! = 26 x 25 x 24 x 23 x 22... = 403291461126605635584000000

(26 - 5)! = 21! = 51090942171709440000

An easy hack for solving division of large factorials is to use canceling.

26!/21! = 26 x 25 x 24 x 23 x 22 (because 21 down to 1 is cancelled by 21!)

= 7,893,600