Permutation and CombinationHard
Question
Shubham has to make a telephone call to his friend Nisheeth, Unfortunately he does not remember the 7 digit phone number. But he remembers that the first three digits are 635 or 674, the number is odd and there is exactly one 9 in the number. The maximum number of trials that Shubham has to make to be successful is
Options
A.10,000
B.3402
C.3200
D.5000
Solution
Let the number starts with 635
then two cases arise
Case-1 If 9 occurs at units place
then the number of numbers = 9 × 9 × 9 = 729
Case-2 If 9 does not come at units place.
then number of ways for 9 to occur at either of the rest three places = 3C1 = 3
∴ the number of numbers = 3 × 9 × 9 × 4 = 972
∴ total numbers starting with 635 = 729 + 972 = 1701
Similarly total number starting with 674 = 1701
∴ Maximum number of trials = 1701 × 2 = 3402
then two cases arise
Case-1 If 9 occurs at units place
then the number of numbers = 9 × 9 × 9 = 729
Case-2 If 9 does not come at units place.
then number of ways for 9 to occur at either of the rest three places = 3C1 = 3
∴ the number of numbers = 3 × 9 × 9 × 4 = 972
∴ total numbers starting with 635 = 729 + 972 = 1701
Similarly total number starting with 674 = 1701
∴ Maximum number of trials = 1701 × 2 = 3402
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