SOLUTION: Mrs. Voss’ speech class has 25 students. If 6 students will give their speeches today and the order is chosen randomly, then what is the probability that Tim goes first and Jenny

Question 1191353: Mrs. Voss’ speech class has 25 students. If 6 students will give their speeches today and the order is chosen randomly, then what is the probability that Tim goes first and Jenny goes second (the rest can be anyone)?
*Please use the P(A) = number of outcomes in event A/total number of outcomes formula*
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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Mrs. Voss’ speech class has 25 students. If 6 students will give their speeches today
and the order is chosen randomly, then what is the probability that Tim goes first
and Jenny goes second (the rest can be anyone)?
*Please use the P(A) = number of outcomes in event A/total number of outcomes formula*
~~~~~~~~~~~~~~~~

In this problem, we consider all ordered groups of 6 students, selected from 26 students.


The number of such groups is  25*24*23*22*21*20.

It is the denominator of the fraction: the total number of all possible outcomes.



The favorable outcomes are those ordered groups of 6 students, that have Tim 
at the first position and Jenny at the second position.

The rest 4 students in the group of 6 can be any of remaining 25-2 = 23 students in arbitrary order.

So, the number of favorable groups at this consideration is  23*22*21*20.

It is the numerator of the fraction.



The probability is  

    P =  =  = after canceling common factors =  = .    ANSWER

Solved.

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