Latest TCS Aptitude Question SOLUTION: What is the number of ways of expressing 3600 as a product of three ordered positive integers (abc, bca etc. are counted as distinct). For example, the number 12 can be expressed

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What is the number of ways of expressing 3600 as a product of three ordered positive integers (abc, bca etc. are counted as distinct). For example, the number 12 can be expressed as a product of three ordered positive integers in 18 different ways.
a. 441
b. 540
c. 84
d. 2100

Asked In TCS Deepak Kolte (8 years ago)

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Read Solution (3) :

Ram Vyas  (8 years ago)

3600 = 2^4 × 3^2 × 5^2
Let abc = 2^4 × 3^2 × 5^2
We have to distribute four 2's to three numbers a, b, c in (4+3−1)C(3−1)=6C2 = 15 ways.
Now two 3's has to be distributed to three numbers in (2+3−1)C(3−1)=4C2 = 6 ways
Now two 5's has to be distributed to three numbers in (2+3−1)C(3−1)=4C2 = 6 ways
Total ways = 15 × 6 × 6 = 540

Is this solution Helpfull? Yes (23) | No (1)  

Saunak Das  (8 years ago)

3600=2^4*3^2*5^2... We have to form abc.. So it can be formed by the formula n+r-1c r-1. So total ways 4+3-1c3-1 * 2+3-1c3-1 * 2+3-1c3-1
As we have to make a form of abc , so r=3.
Hence 6c2 * 4c2 * 4c2 = 540.

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biswajit panda  (8 years ago)

answer is 540

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