A five digit number is to be formed using each of the digits 1, 2, 3, 4, 5 and 6 ONLY ONCE.
A five digit number is to be formed using each of the digits 1, 2, 3, 4, 5 and 6 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
Answer/Solution
480
Steps/Work
Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)
6 numbers can be arranged in 6 places in 6! ways. Now tie 1 and 2 together so effectively there are 5 nos. they can be arranged in 5! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 6! - 5!2! = 720 - (120*2) = 480
Answer: E
6 numbers can be arranged in 6 places in 6! ways. Now tie 1 and 2 together so effectively there are 5 nos. they can be arranged in 5! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 6! - 5!2! = 720 - (120*2) = 480
Answer: E