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Railroad Accidents A researcher wishes to study railroad accidents. He wishes to select 3 railroads from 10 Class I railroads, 2 railroads from 6 Class II railroads, and 1 railroad from 5 Class III railroads. How many different possibilities are there for his study?
Intro Stats / AP Statistics
Probability and Counting Rules
Sampling and Data
Missouri State University
University of North Carolina at Chapel Hill
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in this problem a researcher, we just to study the railroad accidents. Those happen in three events in sequence. In first even he took three through railroad accidents from tendril road accidents. In first even we converted as then see three. So it is 10 factorial. Do you read it by then? Minus three factorial in tow three factorial Now you all know the formulae off to find out the number of combinations which can be formed for an objects ed up are objects he can take that is N c are equal toe and factorial do it by end minus r factorial into our factory Let's see 10 factorial is then in tow nine into eight in tow seven Factorial doing it by 10 minus three is seven factorial into our factory is three factorial. You can write it as three in tow. Two into one now seven. Factory is conserved in numerator and denominator! Let's simplify. We'll get 1 20 please Now let's see. Second even. Hey, look to real road accidents out off six plus two real road accidents He's six. See second, even a six Ito so six factorial directed by six minus two factorial into two Factorial is two in tow. One six factory reconverted as six into five in tow. Four in tow, three in tow. Do into one. Divided by six. Minus two is full factorial. So for in tow three in tow doing one in tow to factor. That is two into one. Now we will can sell four factorial in numerator and denominator. We get 15 days for sick and even in third even he took one drill extent out of five last three railroad accidents That statement we conducted in an expression way. Fine, See one equal toe five factorial debated by find minus one factorial into one factorial five factorial is five into for into three into doing to one divided by five minus one is four factorial you converted as for factory in four into three in tow. Doing toe one into one factor really is one. Now we will can sell for factorial in numerator and denominator. So there are five ways to study last three extent here We had to find out all of that, even up this for that By using fundamental counting room. You all know what is fundamental counting rule If some even sir. Happening in sequence. We heard toe multi play. Although events for that even one is then see three into even to is that is close to railroad accidents. 63 62 in tow. Court Even these if I see one No. 10 C three value is 1 20 here. Um, multiplying all the three ways. 1 20 into 15. Indoor five, We'll get 9000.
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