15) How many 4-letter words with or without meaning, can be formed of the word, 'LOGARITHYMS', if repetition of letters is not allowed? a) 720 b) 420 C) 5040 d) 256
Answers
answer is c
Answer
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Hint:
We can take the letters in the given word and count them. Then we can find the permutation of forming 4 letters words with the letters of the given words by calculating the permutation of selecting 4 objects from n objects without replacement, where n is the number of letters in the given word which is obtained by the formula, nPr=n!(n−r)!
Complete step by step solution:
We have the word ‘LOGARITHMS’.
We can count the letters. After counting, we can say that there are 10 letters in the given word.
⇒n=10
Now we need to form four letter words from these 10 numbers. As the words can be with or without meaning, we can take all the possible ways of arrangements.
As the repetition is not allowed, we can use the equation nPr=n!(n−r)! where n is the number of objects and r is the number of objects needed to be selected.
So, the number of four-letter words can be formed is given by,
⇒10P4=10!(10−4)!
So we have,
⇒10P4=10!6!
Using properties of factorial, we can write the numerator as,
⇒10P4=10×9×8×7×6!6!
On cancelling common terms we get,
⇒10P4=10×9×8×7
Hence we have,
⇒10P4=5040
Therefore, the number of four-letter words that can be formed is 5040.
So the correct answer is option C.