Combinations Distinguishable Permutations

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

How many ways can the letters in the word PARALLEL be arranged?

• 40,320
• 1
• 3360
• 64

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

• Counting Principle
• Permutations
• Combinations
• Commutative Property

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
• 1
• 81
• 72

There are 5 stairways and 6 exterior doors.  How many ways can a student choose 1 door and 1 stairway to get from the outside to the 2nd floor, then use a different stairway and exterior door to leave.

• 900
• 600
• 150
• 30

What is the probability of choosing 2 female senators if there are 19 female senators out of 100?

• 342
• 1/342
• 171
• 1/171