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

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## Q-How many four-digit numbers can be formed from the digits 1, 3, 4, 5, 6 and 7, if repetition of the digit is not allowed?… and if the numbers are greater than 5,000?

### Solution

We have 6 digits available.

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There are 3 ways to fill the first digit (5,6,7)

5 ways to fill the second digit

4 ways to fill the third digit

3 ways to fill the fourth digit

3×5×4×3=180

180, four-digit numbers if the numbers are greater than 5,000 can be formed from the digits 1, 3, 4, 5, 6 and 7 where the digits are used repetition is not allowed

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

The first digit can be selected in six ways; and another digit can also be selected in six ways

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Including the third digit increases the number of ways to

36 \times 6=  216.

Note: If repetition is not allowed, the number of ways will be

 6 \times 5 \times 4 = 120

## Q3- How many numbers can be formed from 1, 2, 3, 4, 5 if repetition of the digit is not allowed

the number of total numbers = 5 + 20 + 60 + 120 + 120=325

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