Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I was looking for a combinatorical explenation for this identity $$\sum_{x_1+x_2+x_3 \le18}\binom{18}{x_1,x_2,x_3} = 4^{18}$$ A simple explenation would be enough,

Thanks

share|improve this question

1 Answer 1

This just the multinomial theorem for $(1+a+b+c)^{18}$ where $a = b = c = 1$.

Just leave a comment, if you need a less simple explanation :-)

Edit: Please note, that at Wikipedia's page there's a bit different definition of multinomial than yours, i.e. $\binom{n}{k_1, k_2, k_3}$ as compared to $\binom{n}{k_1, k_2, k_3, k_4}$ where $k_4 = n-k_1-k_2-k_3$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.