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5 Most important question regarding permutations and combinations.

1.Find out the number of words which can form the latter of word 'YELLOW' if repetiation is not allowed.

Solution: Given that a word'YELLOW'in which we have 5 distinct latter such that Y,E,L,O and W.

We want to form word in which 6 latter and repetiation is not allowed.

So we have 6 place such that _ _ _ _ _ _ 

Now the number of way to fill first place = 6

Number of way to fill second place = 5

Number of way to fill the third place = 4

Number of way to fill fourth place = 3

Number of way to fill fifth place = 2

And number of way to fill sixth place = 1.

So required number of words = 6×5×4×3×2×1 = 720.

But here both 'L'are same.

Hence the total number of words = 720/2! = 360.

2.Find out the number of words which can form the latter of word 'BUTTER' if repetiation is not allowed.

Solution: Given that a word 'BUTTER' in which we have 5 distinct latter such that B,U,T,E and R.

We want to form word in which 6 latter and repetiation is not allowed.

So we have 6 place such that _ _ _ _ _ _ 

Now the number of way to fill first place = 6

Number of way to fill second place = 5

Number of way to fill the third place = 4

Number of way to fill fourth place = 3

Number of way to fill fifth place = 2

And number of way to fill sixth place = 1.

So required number of words = 6×5×4×3×2×1= 720

But here both 'T'are same.

Hence the total number of words =720/2!= 360.

3.Find out the number of words which can form the latter of word 'INDIA' if repetiation is not allowed.

Solution: Given that a word 'INDIA' in which we have 4 distinct latter such that I,N,D and A

We want to form word in which 5 latter and repetiation is not allowed.

So we have 5 place such that _ _ _ _ _ 

Now the number of way to fill first place = 5

Number of way to fill second place = 4

Number of way to fill the third place = 3

Number of way to fill fourth place = 2

And Number of way to fill fifth place = 1

So required number of words = 5×4×3×2×1 = 120.

But here both 'I' are same.

Hence the total number of words = 120/2! = 120/2 = 60.

4.Find out the number of words which can form the latter of word 'GOOGLE' if repetiation is not allowed.

Solution: Given that a word 'GOOGLE' in which we have 4 distinct latter such that G,O,L and E.

We want to form word in which 6 latter and repetiation is not allowed.

So we have 6 place such that _ _ _ _ _ _

Now the number of way to fill first place = 6

Number of way to fill second place = 5

Number of way to fill the third place = 4

Number of way to fill fourth place = 3

Number of way to fill fifth place = 2

And Number of way to fill sixth place = 1

So required number number of words = 6×5×4×3×2×1= 720

But here both 'G' and both 'O' are same.

Hence the total number of words = 720/2!×2! = 720/4 = 180.

5.Find out the number of words which can form the word 'BOTTOM' if repetiation is not allowed.

Solution: Given that a word 'BOTTOM' in which we have 4 distinct latter such that B,O,T and M.

We want to form word in which 6 latter and repetiation is not allowed.

So we have 6 place such that _ _ _ _ _ _

Now the number of way to fill first place = 6

Number of way to fill second place = 5

Number of way to fill the third place = 4

Number of way to fill fourth place = 3

Number of way to fill fifth place = 2

And Number of way to fill sixth place = 1

So required number number of words = 6×5×4×3×2×1 = 720

But here both 'T' and both 'O' are same.

Hence the total number of words = 720/2!×2!= 720/2×2 = 180.

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