Emily is having a birthday party. a. There are 25 kids in Emily’s class (including herself). Her best friends Joe, Millie and Ray are in her class. For her birthday, she would like to invite 7 children from her class (not counting herself). She invites Joe, Millie and Ray and 4 other children. How many different combinations are possible? b. Each of the kids at the party (including the host Emily) is given one of the eight colored t-shirts that Emily's mother has purchased for the kids (green, blue, orange, red, yellow, pink, 2 x purple). In how many ways can the t-shirts be distributed to the children? c. There is a big bucket with purple, blue, green, yellow, orange and red lollies (hundreds of each color). The green lollies are the tastiest. One after the other, the children throw a colored dice (with six faces corresponding to the colors above), until each child has rolled the dice once. What is the probability that more than 3 children get a green lolly?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Emily is having a birthday party.
a. There are 25 kids in Emily’s class (including herself). Her best friends Joe, Millie and Ray are in her class. For her birthday, she would like to invite 7 children from her class (not counting herself). She invites Joe, Millie and Ray and 4 other children. How many different combinations are possible?
b. Each of the kids at the party (including the host Emily) is given one of the eight colored t-shirts that Emily's mother has purchased for the kids (green, blue, orange, red, yellow, pink, 2 x purple). In how many ways can the t-shirts be distributed to the children?
c. There is a big bucket with purple, blue, green, yellow, orange and red lollies (hundreds of each color). The green lollies are the tastiest. One after the other, the children throw a colored dice (with six faces corresponding to the colors above), until each child has rolled the dice once. What is the probability that more than 3 children get a green lolly?
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