If the integers m and n are chosen at random between 1 and 100 , then the probability that a number of the form 7^m+7^n is divisible by 5 , equals

Step-by-step solution

Since, m and n are selected between 1 and 100 , hence sample space =100 100 Also, 7^1=1,7^2=49,7^3=343,7^4=24017^5=16807 etc. Hence, 1, 3, 7 and 9 will be the last digits in the power of 7 . Hence, for favourable cases. array lllllll c nm && & & 1,2 & 1,2 & 1,3 & & 1,100 & 2,1 & 2,2 & 2,3 & & 2,100 100,1 & 100,2 & 100,3 & & 100,100 array favourable cases =25 for m=2, n=4,8,12,10 100 favourable cases =25 Similarly for every m , favourable n are 25 . Total favourable cases =100 25 Hence, required probability = 100 25