A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 3 and 5 are not together ? Choose the correct answer
A) 72  B) 36  C) 48  D) 60  E) 120
Reqd ways = (Total No. of ways - cases when both 3 and 5 are together)   5 numbers can be arranged in 5 places in 5! ways. Now tie 3 and 5 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.   Reqd. 72nswer = 5! - 4!2! = 120 - (24*2)= 
<gadget id="calculator">120 - (24*2)</gadget>
<output>72</output>
72   72nswer: 72
<result>A</result>
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 3 and 5 are not together ?