Question

9. There are nine slips of paper numbered from 1 to 9 in a bag. Four slips are randomly selected without replacement to form a 4-digit number.

a. How many 4-digit numbers can be formed?
b. How many 4-digit numbers start with the digit 1?

Answer 1

3024 numbers

336 numbers

Explanation:

There are nine slips of paper numbered from 1 to 9 in a bag. Four slips are randomly selected without replacement to form a 4-digit number.

First digit is selected in 9 ways

now we have only 8 papers

second digit is selected in 8 ways

third digit is selected in 7 ways

fourth digit is selected in 6 ways

4 digit numbers =
`9 \cdot 8 \cdot 7 \cdot 6 =3024` numbers

first digit is selected in only one way

second digit is selected in 8 ways

third digit is selected in 7 ways

fourth digit is selected in 6 ways

4 digit numbers =
`1 \cdot 8 \cdot 7 \cdot 6 =336` numbers