Difference between revisions of "Multinomial Theorem"
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<math>\binom{n}{k_1,k_2,\cdots,k_x}=\dfrac{n!}{k_1!k_2!\cdots k_x!}</math> | <math>\binom{n}{k_1,k_2,\cdots,k_x}=\dfrac{n!}{k_1!k_2!\cdots k_x!}</math> | ||
+ | ==Problems== | ||
+ | ===Introductory=== | ||
+ | ===Intermediate=== | ||
+ | *The expression | ||
− | + | <math>(x+y+z)^{2006}+(x-y-z)^{2006}</math> | |
− | + | is simplified by expanding it and combining like terms. How many terms are in the simplified expression? | |
+ | |||
+ | <math> \mathrm{(A) \ } 6018\qquad \mathrm{(B) \ } 671,676\qquad \mathrm{(C) \ } 1,007,514</math><math>\mathrm{(D) \ } 1,008,016\qquad\mathrm{(E) \ } 2,015,028</math> | ||
+ | |||
+ | -([[2006_AMC_12A_Problems/Problem_24|2006 AMC 12A Problem 24]]) | ||
+ | ===Olympiad=== | ||
{{stub}} | {{stub}} |
Revision as of 20:54, 24 September 2007
The multinomial theorem states that
where
Contents
[hide]Problems
Introductory
Intermediate
- The expression
is simplified by expanding it and combining like terms. How many terms are in the simplified expression?
Olympiad
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