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

Step-by-step 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 :-

$^{10}P_4=\frac{10!}{(10-4)!}=\frac{10\times9\times8\times7\times6!}{6!}\\\\=10\times9\times8\times7=5040$

Hence, the  number of possible passwords formed = 5040.

Answer 2

Answer:  B) 5040

Step-by-step 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 = $10_P_4$

=$\frac{10!}{(10-4)!}$

= $\frac{10!}{6!}$

= $\frac{10\times 9\times 8\times 7\times 6!}{6!}$

= 10 × 9 × 8 × 7 = 5040

Thus, The required possible password is 5040.