Science stream knowledge

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 and 4 if repetiation is not allowed.

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

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 = 4 (excluding 0)

Number of way to fill decimal digit place = 4

And the number of way to fill unit digit place = 3

Hence the total number of 3 digits place = 4×4×3 = 48.

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

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

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 = 4 (excluding 0)

Number of way to fill decimal digit place = 5

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

Hence the total number of 3 digits place = 4×5×5 = 100.

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

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

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 = 4 (excluding 0)

Number of way to fill hundred digit place = 4

Number of way to fill decimal digit place = 3

And the number of way to fill unit digit place = 2

Hence the total number of 4 digits place = 4×4×4×3 = 192.

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

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

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 = 4 (excluding 0)

Number of way to fill hundred digit place = 5

Number of way to fill decimal digit place = 5

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

Hence the total number of 4 digits place = 4×5×5×5 = 500.

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

Solution: Given the 5 digit such that 0,1,2,3 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 = 4 (excluding 0)

Number of way to fill thousand digit place = 4

Number of way to fill hundred digit place = 3

Number of way to fill decimal digit place = 2

And the number of way to fill unit digit place = 1

Hence the total number of 5 digits place = 4×4×3×2×1 = 96.