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 5 Most important question regarding permutations and combinations with best concept.

1.Find out the 3 digit numbers which can form the digit 0,1,2,3,4,5,6 and 7 if repetiation is not allowed.

Solution: Given the 8 digit such that 0,1,2,3,4,5,6 and 7.

Now we want to form 3 digit number so we have 3 places such that _ _ _

Because here repetiation is not allowed.

So the number of way to fill hundred digit place = 7 (excluding 0)

Number of way to fill decimal digit place = 7

And the number of way to fill unit digit place = 6

Hence the total number of 3 digits place = 7×7×6 = 294.

2.Find out the 3 digit numbers which can form the digit 0,1,2,3,4,5,6 and 7 if repetiation is allowed.

Solution: Given the 8 digit such that 0,1,2,3,4,5,6 and 7.

Now we want to form 3 digit number so we have 3 places such that _ _ _

Because here repetiation is allowed.

So the number of way to fill hundred digit place = 7 (excluding 0)

Number of way to fill decimal digit place = 8

And the number of way to fill unit digit place = 8

Hence the total number of 3 digits place = 7×8×8 = 448.

3.Find out the 4 digit numbers which can form the digit 0,1,2,3,4,5,6 and 7 if repetiation is not allowed.

Solution: Given the 8 digit such that 0,1,2,3,4,5,6 and 7.

Now we want to form 4 digit number so we have 4 places such that _ _ _ _

Because here repetiation is not allowed.

So the number of way to fill thousand digit place = 7 (excluding 0)

Number of way to fill hundred digit place = 7

Number of way to fill decimal digit place = 6

And the number of way to fill unit digit place = 5

Hence the total number of 4 digits place = 7×7×6×5 = 1470.

4.Find out the 4 digit numbers which can form the digit 0,1,2,3,4,5,6 and 7 if repetiation is allowed.

Solution: Given the 8 digit such that 0,1,2,3,4,5,6  and 7

Now we want to form 4 digit number so we have 4 places such that _ _ _ _

Because here repetiation is allowed.

So the number of way to fill thousand digit place = 7 (excluding 0)

Number of way to fill hundred digit place = 8

Number of way to fill decimal digit place = 8

And the number of way to fill unit digit place = 8

Hence the total number of 4 digits place = 7×8×8×8 = 3584.

5.Find out the 5 digit numbers which can form the digit 0,1,2,3,4,5,6 and 7 if repetiation is not allowed.

Solution: Given the 8 digit such that 0,1,2,3,4,5,6  and 4.

Now we want to form 5 digit number so we have 5 places such that _ _ _ _ _

Because here repetiation is not allowed.

So the number of way to fill ten thousand digit place = 7 (excluding 0)

Number of way to fill thousand digit place = 7

Number of way to fill hundred digit place = 6

Number of way to fill decimal digit place = 5

And the number of way to fill unit digit place = 4

Hence the total number of 5 digits place = 7×7×6×5×4 = 5880.

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