Voting In the 75th Congress (1937-1939) the U.S. House of Representatives had 333 Democrats, 89 Republicans, and 13 members of other parties. Suppose that a bill passed the House with 31 more votes in favor than against, with 10 times as many Democrats voting for the bill as Republicans, and with 36 more non-Democrats voting against the bill than for it. If every member voted either for the bill or against it, how many Democrats, how many Republicans, and how many members of other parties voted in favor of the bill?

A committee is to be formed with a president, vice-president, and a secretary. There are 10 people to be selected from. How many committees are possible?

A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members and any member can be elected to each position? No person can hold more than one office.

A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra-large. If it has 2 small, 3 medium, 6 large, and 2 extra-large in stock, How many orders can it sell all the shirts? Suppose the store decides not to sell the extra-large shirts. In how many orders can it sell the remaining shirts?

Suppose that in a survey of five-year-olds, 49%49% liked the letter A, 56% liked the letter B, and 53% liked the letter of C. 29% liked A and B 29% liked A and C, 32% liked B and C, and 16% liked all of them. What percentage liked A and B but not the letter C?

2. Molly really enjoyed country music. After listening one afternoon to her favorite station foran hour, she had heard 25 songs. All but 1 song were about either truck drivers, being in love,hound-dog owners, or some combination of the three. She noted the following information: Allof the truck drivers were in love. Three-fourths of the truck drivers were not hound-dogowners. There were six hound-dog owners who were in love. Of the hound-dog owners whowere not truck drivers, half of them were in love. Eighty percent of all the songs concernedpeople in love. How many songs concerned people who were in love but were neither truckdrivers nor hound-dog owners?

A town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of four representatives from the seven-member town council, three members of a five-person citizens advisory board, and three of the 11 police officers on the force. How many ways can that committee be formed? That committee can be formed in ways.

A survey of 80 people finds:42 like Metallica.27 like Queen.5 like Nickelback.15 like both Metallica and Queen1 Like both Metallica and Nickelback.2 Like both Queen and Nickelback.1 Likes all three.How many people like Metallica, but neither of the other two bands?

Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men?

The annual National No Spying Day is celebrated at KAOS headquarters this year. There are 11 Control agents and 14 KAOS agents attending. How many ways can we choose a team of 9 agents if 3 team members need to be from Control and 6 from KAOS? (Trivia note: the spying agencies are from Get Smart, a TV series from the late 1960's. I only watched it in reruns :-) --Dr. N.) How many ways can we choose a team of 9 agents if at least 1 team member needs to be from Control?