Question

how many arrangements can be made using all the letters of the word madam

Answer 1

MADAM-It is a 5 letter word.

                 So in 5 places we can use the 5 letters in 5! ways

                 How?5?

                  _ _ _ _ _  ->Consider these 5 underscores represent 5 places where letters need to be filled.

                 1st place-5 letters can be filled

                 2nd place-4 letters can be placed(bcs already 1 letter is occupied by 1st place)      

                 3rd place-3 letters

                 4th place-2 letters

                 5th place-1 letter

                 Totally-5*4*3*2*1=5!

                 But in the word MADAM,M and A are repeating.

                 So it need to be neglected by dividing  2! for M 2! for A

                 Thus 5!/(2! * 2!)=(5*4*3*2*1)/4

                                            =30

                  In 30 number of ways this letter can be rearranged.