Question

Find the numbers of all 4-lettered words ( not necessarily having meaning ) that can be formed using the letters of the word BOOKLET.​

Answer 1

Answer:

480!!!

Step-by-step explanation:

Now the word BOOKLET, has 6 different letters B, O, K, L, E, T and letter O has 2 occurrences.

Your task is to find the number of 4-letter words using the above letters.

Now I split the problem into 2 cases, where first I find the number of 4-letter words having 2 ‘O’s in it and secondly find the number of 4-letter words with either 1 ‘O’ or no ‘O’s.

Case 1 :

Firstly, the number of ways of finding 2 places out of 4 is 4C2 = 6.

In each selection of 2 places, since you fill two identical letters ‘O’ therefore no other way of arrangement is possible.

Now the remaining 2 places must be filled by B, K, L, E, T. There are 5 letters and 2 places to be filled, hence the first place can be filled in with 5 letters and second place with remaining 4 letters, so number of ways is 5*4 = 20.

Therefore the number of 4-letter words having 2 ‘O’s will be 6*20 = 120.

Case 2 :

In this case you have can either use 1 ‘O’ or no ‘O’s, so the letters are B, O, K, L, E, T which needs to be fill 4 spots and note here that we are only using one ‘O’ over here. Hence the first spot can use 6 letters, second spot can use remaining 5 letters, third will use remaining 4, and fourth spot will use remaining 3 letters.

Therefore the number of 4-letter words having no ‘O’s or 1 ‘O’S will be 6*5*4*3 = 360.

Now, the total number of such words as given in the question is given by adding the result of both the cases which is 120 + 360 = 480.

Hence the answer is 480.

Hope it helped.

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