Combination Word Problems

Using 5 consonants and 4 vowels, how many words of 2 consonants and 2 vowels can be formed (hint: the letters must be chosen, then arranged)?

• 1400

• 1420

• 1440

• 1460

In a group of 5 boys and 4 girls, three children are to be selected. In how many different ways can they be selected such that at least two girls should be there?

• 44
• 34
• 24
• 14

There are 6 men and 5 women and you need to form a committee of a man and a woman. In how many ways can the committee be formed?

• 30
• 36
• 40
• 64

A school committee of 5 is to be formed from 12 students. How many committees can be formed if Paul must be on the committee?

• 325

• 330

• 335

• 340

A lottery has 45 numbers and you must pick 6 numbers. How many different combinations are possible if your lucky numbers 11 and 42 must be on the lottery ticket?

• 123,380

• 123,390

• 123,400

• 123,410

There are 6 meats and 10 veggies available to make a sandwich. How many sandwiches have 3 meats and 5 veggies?

• 5,020

• 5,030

• 5,040

• 5,050

A student council of 5 members is to be formed from a selection pool of 8 boys and 9 girls. How many committees will have at most 2 boys?

• 3,486

• 3,490

• 3,496

• 3,502

From a deck of 52 cards, how many 5 card hands have at least two red cards?

• 2,144,470

• 2,144,480

• 2,144,490

• 2,144,500

A research team of 6 people is to be formed from 10 chemists, 5 statisticians, 8 economists, and 15 biologists. How many teams have at least 5 chemists?

• 7,248

• 7,254

• 7,260

• 7,266

From a deck of 52 cards, how many 5 card hands have at most 3 kings?

• 2,598,904

• 2,598,908

• 2,598,912

• 2,598,916