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Nine people can be selected from the group of 12 in
(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4) = 79,833,600ways.
But each group of the same 9 people can be selected in
(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 362,880 different orders.
So the number of different 9-person committees that can be selected is
79,833,600/362,880 = 220 .
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How many ways can you arrange 4 out of 8 books on a shelf?
There are 8 ways to choose the first book There are 7 ways to choose the second book - 8 x 7 = 56 ways to select two books There are 6 ways to choose the third book - 8 x 7 x 6 = 336 way to select three books There are 5 ways to choose the fourth book - 8 x 7 x 6 x 5 = 1,680 ways to select four books.
In how many different ways can 5 students be arranged for a group picture if all students must face forward and be in a straight line?
For the first spot, you can choose any one of 5 students. For the second spot, you can choose any one of the remaining 4 students. For the third spot, you can choose any one of the remaining 3 students. etc. So the answer is: 5x4x3x2x1 = 120
How many ways can a committee of 3 people be chosen out of 10 people?
Combination of three people from a group of 10 = (n!)/[r! x (n-r)!], where n = 10 and r = 3. The answer is therefore (10.9.8.7.6.5.4.3.2.1)/[(1.2.3) x (1.2.3.4.5.6.7)] = (10.9.8)/(1.2.3) = 10.3.4 = 120 ways
How many different ways can 10 colored pencils be distributed to a group of 4 art students?
I Dont Know [210]
In how many ways can a committee of 3 be chosen from 10 students?
The answer is 10 over 3 (you write 10 over 3, without a fraction line in between, and with parentheses around the entire expression). This is calculated as (10 x 9 x 8) / (1 x 2 x 3).
