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Evaluate each expression.$$\begin{array}{ll}{\text { a. }_{3} C_{0}} & {\text { d.} _{12}C_{2}} \\ {\text { b. }_{3} C_{3}} & {\text { e. }_{4} C_{3}} \\ {\text { c. }} {\text { gC }_{7}}\end{array}$$

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

University of North Carolina at Chapel Hill

Cairn University

University of St. Thomas

Idaho State University

Lectures

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in this problem, we will evaluate some expressions. So Foster one is three c zero. It's looks like N c R that these n see art N c r is in factorial divided by in minus r factorial in tow. Ofek Dorian Now we will substitute the values off and art. In fact, a real is three factorial on and minus Audi's three minus zero factorial indoor r factorial heart is zero So three effect Auriol, divided by three minus zero is on So three factorial into zero factorial is one we can cancel three factorial in numerator and denominator You'll get 11 divided by one is one. Next one, ease three see three he'll three is and on three is are so entered Our You see him nimble equals toe three factorial dueted by three minus three factorial in tow. Our is three so three factory in three factorial is three in tow Doing to one divided by three minus three is zero factorial You do three Factory is three into doing to one. Now we will cancer three factory in numerator denominator as well. So we will get one. They were led by zero factorial is one so one is the final answer. Next one is nine. See seven he'll and equal to nine and are equal to seven. Once we substitute the values off energy are in the formally well, we can write it as an factorial ease. Nyein Factorial Divided by and minus R factorial is nine minus seven. Factorial into our factory is seven factory so nine into eight into seven factory vibe er stopping hill because and seven factorial is in denominated. Also, it's easy. Vettel simplified out both numerator and denominator. Nine. Minus seven is two factorial and seven factorial. Now we will cancel seven Factory in numerator and denominator nine. Indo it into divided by two Factor really is do into one four times nine multiplied before is 36. Next one is well see do now an equal do 12 and are equal toe and C are equal do in factorial divided by n minus. R. Factorial in tow. R factorial when we substitute the values off and are in the formally we conducted as drill see to equal toe drill factorial divided by drill minus two factorial into two factory full factorial is drill in tow. 11 in two 10 factorial divided by fell minus two. Factorial is 10 factorial into two factory doing do one Now we will cancel 10 factorial in numerator and denominator. When we simplified ill both numerator and denominator, we will get 66 not next. One East four C three. He's speaking rated as four factorial he ordered by four minus three factorial into three. Factory four factorial four indoor three Factorial divided by for ministry is one factorial in 23 Factorial. Now we will cancel both three Factory in numerator and denominator four divided by one factory is one so four is the answer.

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