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Two distinct numbers a and b are chosen randomly from the set {2, 22, 23, 24, ......, 225}. Find the probability that logab is an integer.
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5 Answers
1133No. of ways of selecting a and b is 25C2.2! = 600
No. of ways in which a and b can be chosen such that logbloga is an integer:
[251] - 1 + [252] - 1 + [253] - 1 + [254] - 1 + .... + [2525] - 1 = 62, where [.] is the floor function.
Probability = 62/600 = 31/300
- Akshay Ginodia opps! didnt apply permutations to a&bUpvote·0· Reply ·2014-03-07 22:46:54
- Akshay Ginodia Btw can u plz explain ur solution.? :)
- Sourish Ghosh If you choose any number 'k' b/w 1 and 25 then no. of multiples of k <= 25 is [25/k] - 1. For example take 6. No. of multiples of 6 which is less than 25 is 3 {12, 18, 24} which is [25/6] - 1.
Aditya Agarwal why did you not consider 6 as well?
i mean, if a=6 and, b=6 as well, then also the value of log will be an integer(=1).
Shaswata Roy @Aditya:It has been mentioned in the question that a and b are distinct.
535Why are we permuting?
for eg. if a = 8 and b = 64
logab=2 but for the other case where a=64,b=8 value of the log becomes 0.5?
- Akshay Ginodia we are permuting to get the total number of cases