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.
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
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
| Single digit | 5= \;5\;ways |
| Two digit | 5\times4=\;20\; ways |
| three digit | 5\times4\times 3= \;60\; ways |
| four digit | 5\times4\times 3\times2 =\;120\; ways |
| five digits | 5\times4\times 3\times2\times1= \;120\; ways |
the number of total numbers = 5 + 20 + 60 + 120 + 120=325