How many terms?

Probability Level 3

Let $200! = A \times 10^k$ , where $A$ and $k$ are positive integers , and $A$ is not a multiple of 10.

Find the number of distinct terms in the expansion of $(a+b+c)^k$ .

The answer is 1275.

1 solution

Md Zuhair
Sep 7, 2016

We will see that $200!$ has $49$ zeroes. Then $(a+b+c)^{49}$ . then we will see all the terms are in AP and their sums will be $1275.$

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Calvin Lin Staff - 4 years, 9 months ago

Thank you for the information.

Md Zuhair - 4 years, 9 months ago

How many terms?

The answer is 1275.

1 solution

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