Permutations When All Objects Are Not Distinct

Find the number of different ways of arranging letters in the word ARRANGE. How many of these arrangements the two R’s and two A’s are not together?

How many different 6-digit numbers can be formed using digits in the number 659942? How many of them are divisible by 2?

A coin is tossed 8 times. In how many ways can we obtain at least 6 heads?

Find the number of different ways of arranging letters in the word PLATOON if the two O’s are never together.

Find the number of permutations of letters of the following word: DIVYA

Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N.

A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails?

Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A.