Question

in how many different ways can the letters of the word peanut be arranged so that n always come before p​

Answer 1

Answer:

Step-by-step explanation:in the word peanut there are 6 letters , so the available positions are _ _ _ _ _ _

Given that n is always before p

So ,we have to allot n position first and then the position of p based on n position

FIRST, if n takes 1st position, n_ _ _ _ _

p can take any of the remaining 5 positions

remaining letters ie, e,a,u,t can be arrange in 4! Ways

Second, if n takes 2nd position ,

P can take any of the 4 positions

remaining letters ie, e,a,u,t can be arrange in 4! Ways

Third , if n takes the 3rd position,

P can take any of the three positions

remaining letters ie, e,a,u,t can be arrange in 4! Ways

Fourth, if n takes the 4th position

P can take any of the two remaining positions

remaining letters ie, e,a,u,t can be arrange in 4! Ways

Fifth, if n takes the 5th position

P has only one position that is the 6th position

remaining letters ie, e,a,u,t can be arrange in 4! Ways

So , the number of ways are

5p1.4! + 4p1.4! +3p1.4! +2p1.4! +4!

=4!(5+4+3+2+1)

=15(4.3.2.1)

=360