Question

How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? a. 119 c. 2520 b. 16,807 d. 120 Please select the best answer from the choices provided A B C D

Answer 1

Answer: C. 2520

Step-by-step explanation:

Given digits: 0, 1, 2, 3, 4, 5, 6

Total number of digits=7

The number of ways, in which 5-digit numbers can be formed using the above digits if repetition of digits is not allowed is given by permutation:-

$^7P_5=\frac{7!}{(7-5)!}\\\\=\frac{7\times6\times5\times4\times3\times2!}{2!}\\\\=\frac{5040}{2}\\=2520$

Hence, the number of 5 digit numbers can be formed with the given digits (if repetition is not allowed)=2520

Answer 2

1st digit 1 of 7 numbers

2nd digit 1 of 6 numbers

3rd digit 1 of 5 numbers

4th digit 1 of 4 numbers

5th digit 1 of 3 numbers

7*6*5*4*3 = 2520 combinations