Shubham has to make a telephone call to his friend Nisheeth, Unfortunately he does not remember the

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

Accepted Answer

Let the number starts with 635then two cases ariseCase-1 If 9 occurs at units placethen the number of numbers = 9 &#215; 9 &#215; 9 = 729Case-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&#8756; the number of numbers = 3 &#215; 9 &#215; 9 &#215; 4 = 972&#8756; total numbers starting with 635 = 729 + 972 = 1701Similarly total number starting with 674 = 1701&#8756; Maximum number of trials = 1701 &#215; 2 = 3402

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