Let's learn A B C today

Probability Level 3

If ( x + y ) 2 (x+y)^2 has three terms which are x 2 + y 2 + 2 x y x^2+y^2+2xy , then how many terms does ( a 3 + b 3 + c 3 + d 3 + ⋯ + y 3 + z 3 ) 11 (a^3+b^3+c^3+d^3+\cdots+ y^3+z^3)^{11} will have?

This problem is original.


The answer is 600805296.

Abhay Tiwari by Abhay Tiwari , 28, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Simply the number of distinct terms of ( a 1 + a 2 + a 3 + ⋯ + a n ) m (a_1+a_2+a_3+\cdots+a_n)^m is given by ( m + n − 1 n − 1 ) \binom{m+n-1}{n-1} .

So we need ( 36 25 ) = 600805296 \binom{36}{25}=\boxed{600805296}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...