How many numbers greater than 4000 can be formed with the digits 1,2, 3, 4,5 no digit being repeated

1 digit numbers: can't do because we need the number to be bigger than 100 2 digit numbers: can't do because we need the number to be bigger than 100 3 digit number: so numbers like 123 or 345. We have 5 choices and 3 slots, so P(5,3) = (5!)/(5-3)! = (5!)/(2!) = 120/2 = 60. There are 60 different 3 digit numbers 4 digit numbers: P(5,4) = (5!)/(5-4)! = (5!)/(1!) = 120/1 = 120. There are 120 different 4 digit numbers 5 digit numbers: P(5,5) = (5!)/(5-5)! = (5!)/(0!) = 120/1 = 120. There are 120 different 5 digit numbers ------------------------------------------------------------------------- Add up the results: 60+120+120 = 300

There are 300 different numbers that can be formed that are greater than 100. These numbers either have 3 digits, 4 digits or 5 digits.

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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