Global Lehigh Strategic Initiatives (without descriptions)
6th Grade Math Notes One Step Equations
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5. Example 2: how many ways can u give 3 cans to 8 kids?The order of the cans does not matter so we have a combinationSince there r 8 kids….u can choose 8 different kids for the 1st can, 7 kids for the 2nd can, & 6 kids for the 3rdSo far your combination looks like this 8 x 7 x 6..Since we r using 3 cans we must divide by 3! (3 factorial)So we now have 8 x 7 x 6 divided by 3! = 336/6 = 56 ways to give 3 cans.If a problem is a combintation then the order of the items does not matter.For example if you were to make teams of 2 from matt, sara, tim, rob, and ally……then the team of tim & rob is the same as rob & tim Therefore in this case order does not matter and the problem would be a combination.To solve combinations you must use factorials…..4 factorial (4!) = 4 x 3 x 2 x 1 and 5 factorial (5!) = 5 x 4 x 3 x 2 x 1In combinations u must divide by the factorial of the # in each team or group to get rid of duplicate groups like team rob/tim & team tim/robExample 1: how many teams of 2 can u make from sara, tim, rob, and ally?Since there r 4 kids….u can choose 4 different kids for the 1st spot on the team and then 3 kids for the 2nd spot on the team….So far your combination looks like this 4 x 3..Now we r choosing teams of 2 so we must divide by 2! (2 factorial)So we now have 4 x 3 divided by 2! = 12/2 = 6 teams of 2.Combinations