Indian Institute of Foreign Trade 2008 Solved Paper

Case 2: When we win by uncovering just 3 spots.
_ _ P _ _ _ _ _ _ _
From the first two uncovered spots 1 will show up P. Out of remaining 7 spots, 3 spots will be filled by No prize.
Total number of ways = 2C1*7C3*5!
Case 3: When we win by uncovering just 4 spots.
_ _ _ P _ _ _ _ _ _
From the first three uncovered spots 1 will show up P. Out of remaining 6 spots, 3 spots will be filled by No prize. Total number of ways = 3C1*6C3*5!
Case 4: When we win by uncovering just 5 spots.
_ _ _ _ P _ _ _ _ _
From the first four uncovered spots 1 will show up P. Out of remaining 5 spots, 3 spots will be filled by No prize. Total number of ways = 4C1*5C3*5!
Case 5: When we win by uncovering just 6 spots
_ _ _ __ P _ _ _ _
From the first five uncovered spots 1 will show up P.
Out of remaining 4 spots, 3 spots will be filled by No prize. Total number of ways = 5C1*4C3*5!
Case 6: When we win by uncovering just 7 spots.
_ _ _ _ _ _ P _ _ _
From the first six uncovered spots 1 will show up P. Out of remaining 3 spots, 3 spots will be filled by No prize.
Total number of ways = 6C1*3C3*5!
Hence, the probability that a customer will win =

(10!)

(2!*3!)

=

(3!*2!*5!(56+70+60+40+20+6))

10!

⇒10.Therefore, option A is the correct answer.