Paragraph: Consider the number N =10800 . Question: Number of ordered triplets (x, y, z) of positive integers such that x y z=N , is

Step-by-step solution

(i) Clearly, 2 element set a , b = Number of divisors of N 2 = 5 4 3 2 =30 . Ans. (ii) 10800=2^4 3^3 5^2 Consider a, b, c as beggars and powers on 2,3 and 5 as identical objects to be distributed in a, b, c. Hence number of ways is [ array ll ^6 C ₂ & O O O O ^5 C ₂ & O O O ^4 C ₂ & O O array . Total =15 10 6=900 . Ans. NOTE: ⁶⁰ C ₂ is wrong because if we take two divisiors as 2^3 3^3 5^2 and 2^4 3^3 5^2 then their product will exceed the number 10800. aligned & (iii) Sum = (2+2^2+2^3+2^4 ) (3^1+3^2+3^3 ) (1+5^1+5^