Question

A website requires a four-digit numerical password in which the digits cannot repeat. How many possible passwords are there? . . A) 24. B) 5,040. C) 151,200. D) 3,628,801

Answer 1

Answer: b) 5040

Explanation:

Given: A website requires a four-digit numerical password in which the digits cannot repeat.

Total number of digits (0,1,2,3,4,5,6,7,8,9)=10

By permutation , the number of possible passwords is given by :-

`^(10)P_4=(10!)/((10-4)!)=(10*9*8*7*6!)/(6!)\\\\=10*9*8*7=5040`

Hence, the number of possible passwords formed = 5040.

Answer 2

Answer: B) 5040

Explanation:

Since total number of digits are 10 ( which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

And, According to the question, website requires a four-digit numerical password in which the digits cannot repeat.

Therefore, required possible arrangement =
`10_P_4`

=
`(10!)/((10-4)!)`

=
`(10!)/(6!)`

=
`(10* 9* 8* 7* 6!)/(6!)`

= 10 × 9 × 8 × 7 = 5040

Thus, The required possible password is 5040.