The number of 4-letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is _______.Correct answer is '2454'. Can you explain this answer?

Question

Answer

"EXAMINATION" has letter distribution as follows:

Case-I: When all letters are different
⇒

Case-Il: When two letters are same and two letters are different
⇒

Case-Ill: When two letters are same of one kind and two letters are same of other kind
⇒

Total ways = 1680 + 756 + 18
= 2454

Answer

"EXAMINATION" has letter distribution as follows:

Case-I: When all letters are different
⇒

Case-Il: When two letters are same and two letters are different
⇒

Case-Ill: When two letters are same of one kind and two letters are same of other kind
⇒

Total ways = 1680 + 756 + 18
= 2454

Answer

Number of 4-letter words from the letters of the word 'EXAMINATION'

To find the number of 4-letter words that can be formed from the letters of the word 'EXAMINATION', we need to consider the number of ways we can select 4 letters from the available letters and arrange them in a word.

Step 1: Analyzing the given word

The given word 'EXAMINATION' has a total of 11 letters.

Step 2: Counting the number of ways to select 4 letters

To select 4 letters from the 11 available letters, we use the combination formula. The formula for combination is:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of items, and r is the number of items to be selected.

In this case, n = 11 (total number of letters) and r = 4 (number of letters to be selected).

Using the combination formula:

C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 330

So, there are 330 ways to select 4 letters from the given word.

Step 3: Counting the number of ways to arrange the selected letters

Once we have selected 4 letters, we need to arrange them to form a 4-letter word. Since the order matters, we use the permutation formula. The formula for permutation is:

P(n, r) = n!

Where n is the total number of items, and r is the number of items to be arranged.

In this case, n = 4 (selected letters) and r = 4 (number of letters to be arranged).

Using the permutation formula:

P(4, 4) = 4!

= 4 * 3 * 2 * 1
= 24

So, there are 24 ways to arrange the selected 4 letters.

Step 4: Calculating the total number of 4-letter words

To find the total number of 4-letter words, we multiply the number of ways to select 4 letters by the number of ways to arrange them.

Total number of 4-letter words = Number of ways to select 4 letters * Number of ways to arrange them
= 330 * 24
= 7920

Therefore, the number of 4-letter words that can be formed from the letters of the word 'EXAMINATION' is 7920.

However, the correct answer given is '2454'. Since the given answer is different, there might be some additional restrictions or considerations not mentioned in the question. Without further information, it is difficult to determine the correct answer.

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