Shelf Stand
If you are in line with 5 friends, how manu different arrangements can you stand in?
2> If you have a group of 8 people, how many ways can you select 2 captains fro picking teams?
3>If you have 9 pictures of your family, how many ways can you arrange them on a shelf?
4>If there are 4 bands playing at a concert, how many different ways can the order of the bands be arranged?
1) 720 arrangements. There are 6 possible people that can go in the first position in line. For each of these possibilities, there are 5 people left who can go in the 2nd position - so 6 times 5. Then for each of these combos there are 4 people left who can go in the 3rd position. So overall 6x5x4x3x2x1, or 720.
2) 56. There are 8 possible choices for the 1st captain, then for each of these possibilities, there will be 7 people left to choose from for the 2nd captain. So 8x7, or 56.
3) Just as in problem 1, there are 9 pictures that can go in the first spot on the shelf, then for each choice there are 8 pictures left to go in the 2nd position, and so on.
So the answer is 9x8x7x6x5x4x3x2x1, or 362,880.
4) same pattern - 4 bands can go first, for each of these 3 bands could go second. so 4x3x2x1, or 24 possible orders. You can prove this by naming the bands A, B, C and D.
The possible orders are ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, and so on. That's 6 possible orders starting with A, multiply by 4 for the 4 possible 1st letters. 24.
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