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 a four digit number of the form abcd then c equal?

Answer 1

Hint: In order to solve this problem we need to do arrangements of the 4 digit numbers in which one of the places must contain 9 and the number is odd. It means the last number is among anyone of the numbers 1, 3, 5, 7, or 9. Solving like this will take you to the right answer.

Complete step-by-step answer:
There are 2 ways for arrangement of last 4 digits and those can be:
1) 7th place is the last place with 9 and 4th, 5th, 6th place with numbers 0 to 8.
Therefore we can say that the permutation for the above condition = 9 x 9 x 9 = 729.
Since here we have 9 numbers and 3 places.
2) Not taking 9 at 7th place and putting 1,3,5 or 7 any one of them at 7th place has 4 ways and their arrangement has 3 ways and similar in left three place one place will be for 9 and other 2 place will be arranged in =9×9=81
Therefore the permutation for above criteria = 81 x 4 x 3 = 972
Adding both = 729 + 972 = 1701
Now we need to consider first 3 places can be 635 or 674 so 2 ways as given
Successful or total attempt =2×1701 = 3402 ways
abcd3402
Hence we can clearly see from above that the value of c is 0.

Note: Whenever you get to solve such problems you need to understand the main things here those are, first three numbers can have two arrangements, the last number will always be odd and among those 4 numbers anyone of the number is 9 so you need to keep in mind that using last condition you already have get the arrangement when last number is 9 so you have to consider only 1, 3, 5, 7 at last and get the number of arrangements. So, whenever you get such problems you need to use all the conditions provided and use permutation for arrangements and combination for selection. Students generally make this mistake. Taking care of such things will get your problem solved.