Solve the problem?

Question

How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?

Answer 1

now to chose first digit u can use any of the 7 digits & hence the first digit can be selected in 7 ways


since repetitions are not allowed u cannot use the digit used in the first place & hence u hav only 6 digits to choose from & the second digit can be selected in 6 ways only


similarly for the third digit u hav only five digit to sellect from& hence u can select the 3rd digit in 5 ways

& 4th digit can be selected in 4 ways
& 5th digit can be selected in 3 ways

since all events( events of selecting individual digits ) occur simultaneously u should MULTIPLY the no. of ways of selecting each digit

thus
no. of ways = 7 * 6 * 5 * 4 * 3

= 2520

=

Answer 2

The first digit can be any of the seven.
The second digit can be any of the remaining 6
(therefore, there are 7*6 ways of picking the first two digits)
The third digit can be any of the remaining 5
Number of ways to pick the first three: 7*6*5 = 210
and so on.

Answer 3

7 * 6 * 5* 4 * 3 * 2 *1