1 Trinomial Coefficient In class we learned that a version of the Binomial Theor

Question

1 Trinomial Coefficient In class we learned that a version of the Binomial Theorem, where Ca, is the Binomial Coefficient: TL the mumber of ways to take groups of i things at a time from n total. We can generalize this for a trinomial where re! as long as i j k equal n Comment on how this is a reasonable generalization of the Binomial Coefficient. I'm not looking for a deep algebraic or combinatorial argument. Just prove to me that you under stand how this works Then . Find the coefficient of ry7 in (y z17 How many groups of size six can you make with three distinct objects

Explanation / Answer

x^3 y^7 z^7 in (x+y+z)^17

Cn,i,j,k = n! /(i! j! k!)

here n = 17

i = 3 , j = 7 , k= 7

Cn,i,j,k = n! /(i! j! k!) = 17!/ (3! *7! *7!)

= 2333760

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.