How many words of 4 letters with or without meaning be made from the letters of the word English when repetition of letters is not allowed?

Q:

If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.

Answer & Explanation Answer: D) R

Explanation:

The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.

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Related How many words of 4 letters with or without meaning be made from the letters of the word ‘LEADING’, when repetition of letters is allowed?a)4808b)57600c)2401d)57624e)None of theseCorrect answer is option 'D'. Can you explain this answer?

D) 57624Explanation: LEADING is 7 letters.We have 4 places where letters are to be placed.For first letter there are 7 choices, since repetition is allowed, for second, third and fourth letter also we have 7 choices each, so total of 7*7*7*7 ways = 2401 ways.Now for arrangement of these 4 words, we have 4! Ways.

So total of 2401 * 4! Ways.

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Text Solution

Answer : 7

Solution : There are 10 letters in the word LOGARITHMS. So, the number of 4-letter words is equal to the number of arrangements of 10 letters, taken 4 at a time, i.e., `.^(10)P_(4)=5040`.