How many different ways can 9 people be ordered in a line? Please help me find this factorial.

6 Answers

lynn30k's profile pic

lynn30k | High School Teacher | (Level 1) Educator

Posted on

It helps if you think of it this way--there are 9 possible choices for the first person in line.  After that, there are 8 different choices for the second slot, so there are 9x8=72 ways just of arranging people in the first two positions. Continuing, there are 7 choices for the third position, 6 left for the fourth, etc.  Overall, it looks like 9x8x7x6x5x4x3x2x1, or 362,880 ways of arranging the people.  Have fun!

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morrol | High School Teacher | (Level 1) Associate Educator

Posted on

Factorials are not too difficult, and are actually sort of fun.  The way that you get the answer is by multiplying the number one by two, then that amount by three, then that amount by four all the way up to the number you need the factorial for. Your question would look like this:

1 X 2 X 3 X 4 X 5 X 5 X 6 X 7 X 8 X 9 = 362880

Some calculators have a factorial button on them, but if you just have a scientific calculator, just punch in the numbers. 

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

All you have to do is multiple ever number before 9 including 9 to get the amount of choices so:

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880 different choices

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revolution | College Teacher | (Level 1) Valedictorian

Posted on

1st person get 9 choices, 2nd eight, 3rd seven, 4th six, 5th five, 6th four, 7th three, 8th two and 9th one.

So, the choices they have = 1*2*3*4*5*6*7*8*9= 362880 ways