Counting Principle and Combinations

How many ways can we choose the 5 winning lottery numbers from the numbers 1 to 60, when order does not matter?

• 655,381,440
• 5,461,512
• 777,600,000
• 300

How many ways can 5 paintings be arranged on a wall horizontally?

• 120
• 1
• 25
• 10

Which of the following is used when repetition is allowed and order matters?

• Counting Principle
• Permutations
• Combinations

Which of the following is the same as  ₁₀₀C₇ ?

• ₁₀₀P₇ 
• ₇P₁₀₀ 
• 100!
• ₁₀₀C₉₃ 

Find the number of ways 20 volleyball teams can be matched in the first game of a volleyball tournament.

• 380
• 190
• 2,432,902,008,000,000,000
• 20

A typical combination lock is opened with the correct sequence of three numbers between 0 and 49 inclusive. (A number can be used more than once!) What is the probability of guessing those three numbers and opening the lock on the first try?

• 1/117,600
• 1/19,600
• 1/117,649
• 1/125,000

Find the number of batting orders for 9 players.

• 362,880
• 387,420,489
• 3,720,000
• 72

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?

• 11,424,400
• 10,967,424
• 9000
• 90,000

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

How many different radio station names are possible that consist of 4 or 5 letters?

• 456,976
• 11,881,376
• 12,338,352
• 2880