Complete the chart OR use Pascal's triangle to determine how many different combinations of boys and girls are possible in a family with four children and then answer the questions that follow. Use "B" for boy and "G" for girl. Assume the first letter written represents the oldest child; the second letter is the second to the oldest, etc. Give all answers as a fraction OR a percent rounded to one decimal place. (not all blanks will be used on the chart) 4 BOYS 3 BOYS 2 BOYS 1 BOY 0 BOYS What is the total number of outcomes? What is the probability that a family with four children will have 2 girls and 2 boys? What is the probability of having no boys in a family with four children? What is the probability that the oldest is a boy? Predict the number of different boy/girl combinations in a family with 5 kids. Predict the number of different boy/girl combinations in a family with 7 kids. In a family with 7 kids, how many combinations will have at least 3 boys?
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.
Complete the chart OR use Pascal's triangle to determine how many different combinations of boys and girls are possible in a family with four children and then answer the questions that follow. Use "B" for boy and "G" for girl. Assume the first letter written represents the oldest child; the second letter is the second to the oldest, etc. Give all answers as a fraction OR a percent rounded to one decimal place. (not all blanks will be used on the chart)
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4 BOYS |
3 BOYS |
2 BOYS |
1 BOY |
0 BOYS |
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What is the total number of outcomes?
What is the
What is the probability of having no boys in a family with four children?
What is the probability that the oldest is a boy?
Predict the number of different boy/girl combinations in a family with 5 kids.
Predict the number of different boy/girl combinations in a family with 7 kids.
In a family with 7 kids, how many combinations will have at least 3 boys?
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