Question

Find the number of distinct permutations of
the following words
1) MOBILE
2) CORONA​

Answer 1

Answer:

1)When we arrange all the letters, the number of permutations and the factorial of the count of the elements is the same - in this case it's 6! And if the letters were all unique, such as ABCDEF, that'd be the final answer.

However, we have three e's, which means that we'll double and triple count arrangements. To eliminate them, we need to divide by the ways that the three e's can be internally arranged - and that answer is 3!.

And so, putting it together, we get:

6!3!=6×5×4×3!3!=120

2)The word Corona has one C, four I’s, four S’s, two P’s and a total of 11 letters.

The number of all type of arrangements possible with the given alphabets

                       

Let us first find the case when all the I’s together and so take it as one packet or unit. So now we have one M, one unit of four I’s, four S’s, two P’s and a total of 8 units.

Therefore the number of arrangements possible when all the I’s is together

                           

Hence, the distinct permutations of the letters of the word MISSISSIPPI when four I’s do not come together = 34650 – 840 = 33810.