chetan2u wrote:

If the letters of word PARIS are rearranged to form new words, how many of these words have both P ahead of R and A ahead of S?

(A) 5

(B) 6

(C) 10

(D) 15

(E) 30

New question !!!..

This is a Combinatorics problem! We are provided with a five letter word and is asked to find the total number of combinations where P is ahead of R and A is ahead of S.

First set of combinations: Here P and A takes the first two positions, and the remaining three letters takes any of the three positions

1*1*3*2*1 = 6. But note that the positions of P and A can be interchanged, and still meet the condition.

So total words from the first set of combinations is 6*2=12Second set of combinations: Here P (or A) takes the first position and A(or P) takes the third position. In the second position only R (or S if A has been placed in the first position) and I can be placed.

1*2*1*2*1 = 4. But note that the positions of P and A can be interchanged, and still meet the condition.

So total words from the second set of combinations is 4*2=8Third set of combinations: Here P (or A) takes the first position and A(or P) takes the fourth position. In the fifth position S (or R if P is in the fourth position) must be placed.

1*2*1*1*1 = 2. But note that the positions of P and A can be interchanged, and still meet the condition.

So total words from the third set of combinations is 2*2=4Fourth set of combinations: Here P (or A) takes the second position and A(or P) takes the third position. Only I can take the first place.

1*1*1*2*1 = 2. But note that the positions of P and A can be interchanged, and still meet the condition.

So total words from the fourth set of combinations is 2*2=4Fifth set of combinations: Here P (or A) takes the second position and A(or P) takes the fourth position. Only I can take the first place. Only R (or S if A is in the second place) can take the third place.

1*1*1*1*1 = 1. But note that the positions of P and A can be interchanged, and still meet the condition.

So total words from the fifth set of combinations is 1*2=2Total combinations = 12 + 8 + 4 + 4 + 2 = 30Answer is E!**********Please give me Kudos if you think this solution was helpful!!**********