The simplest way to solve this problem is, Total no of cases of arranging 5 people is 5! ways. Out of these, for half of the cases the father will be back of Tim and for half of the cases he will be ahead of Tim. So we need \(\frac{5!}{2}\) = 60 ways.
Or else,
Total no of ways in which Tim will be ahead of his father is:
_F_ _ _ , _ _ F _ _ , _ _ _ F _ , _ _ _ _ F
Tim can take a place ahead of his father in 1+2+3+4 = 10 ways. And remaining 3 people can be arranged is 3! ways = 6 ways. So a total of 10*6 = 60 ways.
The catch here is the question said Tim should be ahead of his father but not "just ahead" of his father. This makes the answer go from 24(if Tim stands just ahead of his father then only 24 ways are possible) to 60.
OPTION :
D
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Regards,
Chaitanya
+1 Kudos
if you like my explanation!!!