Permutations and Combinations 1 Question 3

3. The number of integers greater than 6000 that can be formed using the digits 3,5,6,7 and 8 without repetition is

(2015 Main)

(a) 216

(b) 192

(c) 120

(d) 72

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Answer:

Correct Answer: 3. (b)

Solution:

  1. The integer greater than 6000 may be of 4 digits or 5 digits. So, here two cases arise.

Case I When number is of 4 digits.

Four-digit number can start from 6,7 or 8 .

Thus, total number of 4-digit numbers, which are greater than 6000=3×4×3×2=72

Case II When number is of 5 digits.

Total number of five-digit numbers which are greater than 6000=5!=120

Total number of integers =72+120=192



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