Recall the formula for a number of permutations of n objects _nP_n.
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Practice makes perfect
Assuming there are 14 floats in the parade and their order is chosen at random, we want to find the probability that the float with the soccer team is first and the float with the chorus is second. To find it we will use theoretical probability.
P=Favorable Outcomes/Possible Outcomes
We will start by finding the number of possible outcomes, which is the number of permutations of all 14 floats in the parade. Let's recall the formula for the number of permutations of n objects.
_nP_n=n!
Since there are 14 floats in the parade, in our case n=14. Therefore, the number of possible outcomes is 14!. Next we will look for the number of favorable outcomes. We want the float with the soccer team to be first and the chorus to be second. We need to take into account only the order of the other floats.
14-1-1= 12
We found how many floats there are left beside the ones with the soccer team and the chorus. Therefore, we will calculate the number of permutations of 12 other floats left because the first and the second floats are fixed.
_(12)P_(12)= 12!
We found that the number of favorable outcomes is 12!. This means that we have enough information to calculate the desired probability.
