Grade 11 · Algebra & functions

Binomial theorem and factorials practice

Binomial theorem and factorials is a grade 11 math skill aligned to Common Core standard HSA.APR.C.5: know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 binomial theorem and factorials problems our math games drill.

CCSS HSA.APR.C.515 questions in the bank
Sample questions

Try 8 for free

Question 1easy

What is C(5,2)C(5, 2)?

C(5,2)=5!2!⋅3!=1202⋅6=10C(5,2) = \dfrac{5!}{2! \cdot 3!} = \dfrac{120}{2 \cdot 6} = 10.

Question 2easy

What is 4!4!?

4!=4×3×2×1=244! = 4 \times 3 \times 2 \times 1 = 24.

Question 3easy

What is C(4,1)C(4, 1)?

C(4,1)=4!1!⋅3!=241⋅6=4C(4,1) = \dfrac{4!}{1! \cdot 3!} = \dfrac{24}{1 \cdot 6} = 4.

Question 4easy

What is 3!3!?

3!=3×2×1=63! = 3 \times 2 \times 1 = 6.

Question 5easy

What is C(5,3)C(5, 3)?

C(5,3)=5!3! (5−3)!=10C(5,3) = \dfrac{5!}{3!\,(5-3)!} = 10.

Question 6easy

What is 6!6!?

6!=6×5×4×3×2×1=7206! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720.

Question 7easy

What is C(6,3)C(6, 3)?

C(6,3)=6!3! (6−3)!=20C(6,3) = \dfrac{6!}{3!\,(6-3)!} = 20.

Question 8easy

What is 2!2!?

2!=2×1=22! = 2 \times 1 = 2.

Tests that cover binomial theorem and factorials:
ACTPARCCPSAT/NMSQTDC CAPEGeorgia Milestones
More Grade 11 skills:
Conic sectionsComplex number operationsExponential and log formulasFunction transformationsGeometric sequence equationsLogarithm rulesSequences and seriesAll Grade 11 practice →

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