Question

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

Answer 1

4,536

Step-by-step explanation:

Given,

there are four Different digits in the identification number and the first number cannot be zero.

This comes under arranging the digits from 0-9 selecting 4 different numbers.

Hence the first digit can be arranged in 9 ways (zero shouldn't come and any number from 1-9)

Now for the 2nd digit there are 9 ways to arrange(i.e., any number from 0-9 excluding the number selected for the first digit.)

Now for the third digit any number from 0-9 can be selected excluding the numbers selected for the first two digits. This can be done in 8 ways

Similarly for the fourth digit there are 7 ways

TOTAL : 9×9×8×7

= 4,536.

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