Question

How many 4 digit numbers can be made using 1, 2, 3, 4, 5, 6, and 7 with none of the digits being repeated ? A. 7! B. 840 c. 4! D. 42

Answer 1

Answer:

b.840

Step-by-step explanation:

the number of 4 digit numbers=7*6*5*4=840

Answer 2

Answer:  B. 840

Step-by-step explanation:

Given digits : 1, 2, 3, 4, 5, 6, and 7

Number of digits = 7

If repetition of digits is not allowed, then we use permutations to find the number of ways to arrange them.

Permutation of n things where r things taken at a time is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Now, the number of 4 digit numbers can be made using 1, 2, 3, 4, 5, 6, and 7 will be :-

$^7P_4=\dfrac{7!}{(7-4)!}=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\=840$

Hence, the number of 4 digit numbers can be made using 1, 2, 3, 4, 5, 6, and 7=840