Convert the following products into Factorials: (I) 6•7•8•9•10 & (ii) 2•4•6•8•10 By Ravi Yadav Sir

Convert the following products into Factorials: (I) 6•7•8•9•10 & (ii) 2•4•6•8•10 By Ravi Yadav Sir

convert the following into factorial (1) 5.6.7.8.9.10.1.12 (ii) 2.4.6.8.10.12

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Since there are 12 runners, there are 12 places to be filled.
If a runner finishes in one place, that runner cannot fill another spot.
Therefore this situation is a permutation.
12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
12! = 479,001,600
There are 479,001,600 possible finishes for 12 runners.

What about 0?
To determine the value of 0! it helps to examine the pattern of factorials.

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The Olympic Swim Problem
As I'm writing this, the Summer Olympics in London are happening, and I've been watching a lot of the swimming events. I'm not much of a swimmer myself, so it amazes me how easily the athletes can glide through the water. It's like they're dolphins or something. Anyway, maybe it's because I'm a math teacher, but I often find myself thinking: how many different ways could all eight of these people finish this race? Maybe they'll end up finishing in this order, or maybe like this or maybe even this. We just thought up three different ways they could finish, but there are probably tons more. How many do you think?

If we tried to actually come up with every single outcome, one at a time, it would take days, and we'd probably kill a tree with all the paper we used up. So, let's see if we can come up with a shortcut.

Let's say that the race is still happening, and no one has finished yet. That means that there are eight different possible winners. Maybe Alex will win, or maybe Chris - we don't know; it could be anyone. But once the winner finishes (whoever it is), now there are only seven different people that might get second.

Continuing this pattern would mean that, at this point, there are only six different people that could get third. After third place finishes, there are only five different people that could get fourth. That means four different people could get fifth, three different people could get sixth and there are two different people that might get seventh. Once the first seven people have finished, there's only one person left that might get last, which means that to answer the question of how many different ways this race could end up, we simply have to multiply 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 to find out that there are 40,320 different possible ways for this race to end.