Question

Suppose you want to count the number of​ four-letter passwords that can be formed using the letters in the word NUMBER. The four letters in the password must all be different. Which of the following expressions is true concerning the number of such​ passwords? (A) There are 10 x 9 x 8 x 7 possibiities (B) It is combination question(C) There are 10000 possibilities(D) The password must not follow order matter

Answer 1

Answer:

D.The password must not follow order matter

Step-by-step explanation:

We are given that suppose you want to count the number of four letters password that can be formed using the letters in the word NUMBER.

We are given that all letters in the password must be all different .There is no nothing saying about order so we can make combination without order .

We have to find the number of 4- letter password that can be formed using letters in the word NUMBER.

By using Permutation formula we find the number of 4- letters password that can be formed by using the letters N,M,B,U,E,R.

Permutation formula : The number of arrangements when taken r objects at a time out of n objects

=$\frac{n!}{(n-r)!}$

Total letters in word NUMBER=N,U,M,B,E,R=6

n=6,r=4

Therefore, the number of arrangements  can be made from 6 letters when 4 letters taken at a time =$\frac{6!}{(6-4)!}$

The number of selection can be made from 6 letters when 4 letters taken at a time =$\frac{6!}{(6-4)!}$

The number of selection can be made from 6 letters when 4 letters taken at a time =$\frac{6\times5\times 4\times3 \times 2!}{ 2!}$

$n!=n(n-1)(n-2)(n-3)...........3\cdot.2\cdot.1$

The number of selection can be made from 6 letters when 4 letters taken at a time =360

Option D is correct.

Answer : D.The password must not follow order matter