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26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must have an equal number of girls and boys? 180 n! 27. Prove that C, C-r by using the formula ,C,= rin

26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must have an equal number of girls and boys? 180 n! 27. Prove that C, C-r by using the formula ,C,= rin

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 51SE: Just-For-Kicks Sneaker Company offers an online customizing service. How many ways are there to...
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Answer question 26. The answer is in red. Write out each step and describe what you are doing.
File Edit View History Bookmarks Profiles Tab Window Help Pro My The 15. X The Mat Des G whi G hov 15.1 15. 15. drive.google.com/file/d/1rSoePSEYJMZZURSELCGHv8uPT3m_g0Hn/view page 739. 21. How many 13-card hands having exactly 11 diamonds can be dealt? 57,798 22. How many 13-card hands having exactly 11 cards from any suit can be dealt? 231,192 23. How many 5-card hands having exactly 3 aces and 2 other cards can be dealt? 4512 24. How many 7-card hands having exactly 3 spades, 3 clubs, and 1 heart can be dealt? 1,063,348 25. In how many ways can 4 or more students be selected from 8 students? 163 26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must have an equal number of girls and boys? 180 = n! 27. Prove that C, C- by using the formula C r!(n-r)!* 28. Prove that Cr=n-1C,-1+n-Cr. (Hint: n! = n · (n − 1)!) 19. a. Refer to the binomial theorem on page 541. What is the relationship between the binomial coefficients in the expansion of (a + b)" and the values of C, for r = 0, 1, 2, ..n? C, is the coefficient of a 'b'. - F-0 b. Based on the results of part (a), rewrite the binomial theorem using sigma notation (see Lesson 11-4) and C. (a+b)" Cab 10. Show that the total number of subsets of a set having n clements is 2". (Hint: Each member of the set is or is not selected in forming a subset. Recall that the empty set is defined to be a subset of every set.) Mixed Review Exercises MAY 24 ♫ MacBook Air 15.
Transcribed Image Text:File Edit View History Bookmarks Profiles Tab Window Help Pro My The 15. X The Mat Des G whi G hov 15.1 15. 15. drive.google.com/file/d/1rSoePSEYJMZZURSELCGHv8uPT3m_g0Hn/view page 739. 21. How many 13-card hands having exactly 11 diamonds can be dealt? 57,798 22. How many 13-card hands having exactly 11 cards from any suit can be dealt? 231,192 23. How many 5-card hands having exactly 3 aces and 2 other cards can be dealt? 4512 24. How many 7-card hands having exactly 3 spades, 3 clubs, and 1 heart can be dealt? 1,063,348 25. In how many ways can 4 or more students be selected from 8 students? 163 26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must have an equal number of girls and boys? 180 = n! 27. Prove that C, C- by using the formula C r!(n-r)!* 28. Prove that Cr=n-1C,-1+n-Cr. (Hint: n! = n · (n − 1)!) 19. a. Refer to the binomial theorem on page 541. What is the relationship between the binomial coefficients in the expansion of (a + b)" and the values of C, for r = 0, 1, 2, ..n? C, is the coefficient of a 'b'. - F-0 b. Based on the results of part (a), rewrite the binomial theorem using sigma notation (see Lesson 11-4) and C. (a+b)" Cab 10. Show that the total number of subsets of a set having n clements is 2". (Hint: Each member of the set is or is not selected in forming a subset. Recall that the empty set is defined to be a subset of every set.) Mixed Review Exercises MAY 24 ♫ MacBook Air 15.
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