Hi Teachers,

Please help me with the below maths questions,

Q1). A comparison of five major credit cards showed that:

• 3 offered cash advances.
• 3 offered extended payments for all goods and services purchased.
• 2 required an annual fee of less than $35.
• 2 offered both cash advances and extended payments.
• 1 offered extended payments and had an annual fee less than $35.
• No card had an annual fee less than $35 and offered both cash advances and extended payments.
• How many cards had an annual fee less than $35 and offered cash advances? (Assume that every card had at least one of the three mentioned features.

Q2)The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 480 graduates:

• 200 had at least 1 year of Spanish.
• 178 had at least 1 year of French.
• 140 had at least 1 year of German.
• 33 had at least 1 year of Spanish and French.
• 24 had at least 1 year of Spanish and German.
• 18 had at least 1 year of French and German.
• 3 had at least 1 year of all three languages.
• How many of the graduates had:
• a. At least 1 year of at least one of the three languages?
• b. At least 1 year of exactly one of the three languages?
• c. Less than 1 year of any of the three languages?

Q3)Two soups, five entres, and three des-serts are listed on the "Special" menu at the Neptune Res-taurant. How many different selections consisting of one soup, one entre, and one dessert can a customer choose from this menu?

Q4)The quality-control department of Starr Communications, a manufacturer of video-game DVDs, has determined from records that 1.5% of the DVDs sold have video defects, 0.8% have audio defects, and 0.4% have both audio and video defects. What is the probability that a DVD purchased by a customer:

a. Will have a video or audio defect?

b. Will not have a video or audio defect?