Question

in how many ways can the letters of the word "problem" be rearranged to make 7 letter words such that none of the letters repeat?

Answer 1

it can be solved using permutation

letters to be used are p,r,o,b,l,e,m

so 1st place can have any of 7                                                                                2nd can have any of the 6 left (letters can't repeat so 1 letter got used in 1st place)

so it follow similarly

and we got the 7*6*5*4*3*2*1=7!=5040

but one of the word will be problem among these 5040 words

so ans is 5040-1=5039