Problem 1: Multiplication Principle, Permutations, and Combinations a) A teacher is going to constitute a team of top 3 students; as president, vice present, and secretary. If there are 10 students, in how many ways can he choose 3 students? b) A teacher is awarding 3 students for scholarships. If there are 10 students, in how many ways can he choose 3 students? c) A baseball team has 15 players. How many 9-player batting orders are possible? d) From a cooler with 8 cans of different kinds of soda, 3 are selected for 3 people. In how many ways can this be done?' e) A group of 4 students is to be selected from a group of 10 students to take part in a class in cell biology. In how many ways can this be done? f) From a group of 15 smokers and 21 nonsmokers, a researcher wants to randomly select 7 smokers and 6 nonsmokers for a study. In how many ways can this study group be selected? g) The college football team has 11 seniors. The team needs to elect a group of 4 seniors co- captains. How many different 4-person groups of co-captains are possible?
Problem 1: Multiplication Principle, Permutations, and Combinations a) A teacher is going to constitute a team of top 3 students; as president, vice present, and secretary. If there are 10 students, in how many ways can he choose 3 students? b) A teacher is awarding 3 students for scholarships. If there are 10 students, in how many ways can he choose 3 students? c) A baseball team has 15 players. How many 9-player batting orders are possible? d) From a cooler with 8 cans of different kinds of soda, 3 are selected for 3 people. In how many ways can this be done?' e) A group of 4 students is to be selected from a group of 10 students to take part in a class in cell biology. In how many ways can this be done? f) From a group of 15 smokers and 21 nonsmokers, a researcher wants to randomly select 7 smokers and 6 nonsmokers for a study. In how many ways can this study group be selected? g) The college football team has 11 seniors. The team needs to elect a group of 4 seniors co- captains. How many different 4-person groups of co-captains are possible?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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Problem 1: Multiplication Principle, Permutations, and Combinations
a) A teacher is going to constitute a team of top 3 students; as president, vice present, and secretary. If there are 10 students, in how many ways can he choose 3 students?
b) A teacher is awarding 3 students for scholarships. If there are 10 students, in how many ways can he choose 3 students?
c) A baseball team has 15 players. How many 9-player batting orders are possible?
d) From a cooler with 8 cans of different kinds of soda, 3 are selected for 3 people. In how many ways can this be done?'
e) A group of 4 students is to be selected from a group of 10 students to take part in a class in cell biology. In how many ways can this be done?
f) From a group of 15 smokers and 21 nonsmokers, a researcher wants to randomly select 7 smokers and 6 nonsmokers for a study. In how many ways can this study group be selected?
g) The college football team has 11 seniors. The team needs to elect a group of 4 seniors co- captains. How many different 4-person groups of co-captains are possible?
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