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Multinomial Coefficients

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StarStarStarStar

(x+y+z)6(x+y+z)^6 term for x3y2z1x^3y^2z^1

StarStarStarStar

6!3!2!1!=60\frac{6!}{3!2!1!} = 60

StarStarStarStar

(x+y)8(x+y)^8 term for x5y3x^5y^3

StarStarStarStar

8!5!3!=56\frac{8!}{5!3!} = 56

StarStarStarStar

(m+n+o+p)5(m+n+o+p)^5 term for m2n2o1m^2n^2o^1

StarStarStarStar

5!2!2!1!0!=60\frac{5!}{2!2!1!0!} = 60

StarStarStarStar

(r+s+t+u)8(r+s+t+u)^8 term for r4s2t1u1r^4s^2t^1u^1

StarStarStarStar

8!4!2!1!1!=840\frac{8!}{4!2!1!1!} = 840

StarStarStarStar

(d+e+f)6(d+e+f)^6 term for d4e1f1d^4e^1f^1

StarStarStarStar

6!4!1!1!=30\frac{6!}{4!1!1!} = 30

StarStarStarStar

(a+b+c+d)7(a+b+c+d)^7 term for a3b2cd1a^3b^2cd^1

StarStarStarStar

7!3!2!1!1!=420\frac{7!}{3!2!1!1!} = 420

StarStarStarStar

(p+q+r)5(p+q+r)^5 term for p2q2r1p^2q^2r^1

StarStarStarStar

5!2!2!1!=30\frac{5!}{2!2!1!} = 30

StarStarStarStar

(u+v+w+x)4(u+v+w+x)^4 term for u1v1w1x1u^1v^1w^1x^1

StarStarStarStar

4!1!1!1!1!=24\frac{4!}{1!1!1!1!} = 24

StarStarStarStar

(v+w+x+y+z)8(v+w+x+y+z)^8 term for v2w2x2y1z1v^2w^2x^2y^1z^1

StarStarStarStar

8!2!2!2!1!1!=2520\frac{8!}{2!2!2!1!1!} = 2520

StarStarStarStar

(a+b+c+d)5(a+b+c+d)^5 term for a2b1c1d1a^2b^1c^1d^1

StarStarStarStar

5!2!1!1!1!=60\frac{5!}{2!1!1!1!} = 60

StarStarStarStar

(x+y+z+w)7(x+y+z+w)^7 term for x3y2z1w1x^3y^2z^1w^1

StarStarStarStar

7!3!2!1!1!=420\frac{7!}{3!2!1!1!} = 420

StarStarStarStar

(m+n)9(m+n)^9 term for m6n3m^6n^3

StarStarStarStar

9!6!3!=84\frac{9!}{6!3!} = 84

StarStarStarStar

(i+j)7(i+j)^7 term for i4j3i^4j^3

StarStarStarStar

7!4!3!=35\frac{7!}{4!3!} = 35

StarStarStarStar

(s+t)10(s+t)^{10} term for s7t3s^7t^3

StarStarStarStar

10!7!3!=120\frac{10!}{7!3!} = 120

StarStarStarStar

(p+q+r+s)6(p+q+r+s)^6 term for p3q1r1s1p^3q^1r^1s^1

StarStarStarStar

6!3!1!1!1!=120\frac{6!}{3!1!1!1!} = 120

StarStarStarStar

(a+b+c)9(a+b+c)^9 term for a3b3c3a^3b^3c^3

StarStarStarStar

9!3!3!3!=1680\frac{9!}{3!3!3!} = 1680

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