X is any 5 digit number formed using the digits 1,2,3,4,5 without repetition. F(X) is evaluated according to the placements of the digits in X- If an odd digit is placed at an odd place, marks received is the digit itself, else 0- If an even digit is placed at an even place, marks received is the digit itself, else 0.F(X) is the sum of marks received in all 5 places of X. for e.g. when X=568, F(X) = 5+6+0 = 11 marks.How many X exists, such that the value of F(X) = 15?
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Step-by-step explanation:
A number divisible by 4 formed using the digits 1,2,3,4 and 5 should have the last two digits 12 or 24 or 32 or 52.
In each of these cases, the five digits number can be formed using the remaining 3 digits in 3!=6 ways.
A number divisible by 4 can be formed in 6×4=24 ways
Total number of 5-digit numbers that can be formed using the digits 1,2,3,4 and 5 without repetition =5!=120
Required probability = 24/120 =
=1/5
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