CAT 1991 — QA Question 13
Permutation & CombinationEasy
How many 3-digit even numbers can you form such that if one of the digits is 5 then the following digit must be 7?
Answer & solution
Correct answer: 365
- A
5
- B
405
365
- D
495
Solution
Case 1: The number has 5 as one of the digits
Three digit number such that 7 follows 5 could be of the form 57_ or _57
Since, the number is an even number
Therefore possible numbers are 570,572,574,576 or 578.
Hence, 5 such numbers are possible.
Case 2: The number does not have 5 as one of the digits
First digit can be fille din 8 ways, second in 9 ways and third in 5 ways (even digits only).
∴ Number of ways = 8 × 9 × 5 = 360
∴ Total number of ways = 5 + 360 = 365
Hence, option (c).