How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?a)720b)420c)5040d)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Since repetition is not allowed, So 3 letters can be selected from 10 letters in 10P3ways=10×9×8=720

Answer

The ans should be 4320 according to me since 10*9*8 is the way we can choose three letters and then 3! is the way these 3 letters can be arranged. So it should be 720*6=4320

Answer

Solution:

To find the number of 3-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition, we need to analyze the given word and the conditions.

Given word: LOGARITHMS

Number of letters in the given word = 10

Number of letters required for each word = 3

Condition: Repetition of letters is not allowed

To solve this problem, we can use the concept of permutations.

Permutations: A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of arrangements of 3 letters taken from the given word without repetition.

The formula to find the number of permutations is:

nPr = n! / (n-r)!

Where n is the total number of objects and r is the number of objects taken at a time.

Step 1: Count the number of distinct letters in the given word.

In the word 'LOGARITHMS', there are 9 distinct letters: L, O, G, A, R, I, T, H, M.

Step 2: Determine the number of ways to choose 3 distinct letters from the 9 distinct letters.

This can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

Where n is the total number of objects and r is the number of objects taken at a time.

In this case, n = 9 and r = 3.

9C3 = 9! / (3! * (9-3)!) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 84

Step 3: Arrange the selected 3 letters in different orders.

For each combination of 3 letters, we can arrange them in 3! = 3 * 2 * 1 = 6 different ways.

Therefore, the total number of 3-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition is:

84 * 6 = 504

So, the correct answer is option B) 504.

Note: The given options do not match the correct answer. The correct answer is not option A) 720.

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