Question

Sam has forgotten his friend's seven-digit telephone
number. He remembers the following: the first three
digits are either 635 or 674, the number is odd, and
the number 9 appears once. If Sam were to use a
trial and error process to reach his friend, what is
the minimum number of trials he has to make before
he can be certain to succeed?
​

Answer 1

Answer:

3402

Step-by-step explanation:

Number can be in form of 635_ _ _ or 674 _ _ _

Consider the following case:

1. Last digit is 9: If last digit is 9 the remaining three place can have 9 digits as   9 can only occur once. So number of ways in which we can guess the number for this case is =   2*9*9*9*1 = 1458

2. Last digit is not 9: If last digit is not 9, then number in the last digit can be any of the remaining odd numbers i.e 1,3,5,7 and also number 9 can be in any of the remaining digits(i.e, position 4, 5, 6 ).So number of ways in which we can guess the number case is = 2*(1*3)*9*9*4 = 1994

Therefore total number of trials required is = 1458 + 1994 = 3402

Note: Since it not mentioned in question that repetition is not allowed, have solved this question by assuming repetition is allowed.