Permutations and Combinations Problems

The video tutorial covers various types of permutations, including linear permutation, permutation with repetition, permutation with identical objects, and circular permutation. Each section explains the rules and provides examples to illustrate the concepts. The tutorial also includes practical applications such as arranging picture frames, creating pin codes, and arranging people around a table.

What is the formula for the number of permutations of n distinct objects taken all at once?

• r factorial

• n plus r factorial

• n minus r factorial

• n factorial

In a linear permutation, how many ways can you arrange 3 picture frames in a row?

• 12

• 9

• 6

• 3

What is the formula for permutations of n distinct objects taken r at a time?

• n factorial divided by (n minus r) factorial

• n factorial times r factorial

• n plus r factorial

• r factorial divided by n factorial

How many ways can 10 cyclists be arranged from first to tenth place?

• 10,000

• 720

• 1,000,000

• 3,628,800

If only the top 3 finalists can move to the national finals, how many ways can the first, second, and third places be awarded?

• 10,000

• 720

• 3,628,800

• 1,000

How many ways can 6 individuals be arranged if there are no seating restrictions?

• 12

• 36

• 120

• 720

If each couple must sit together, how many ways can 3 couples be arranged?

• 120

• 720

• 36

• 12

What is the formula for permutations with repetition?

• n factorial divided by r factorial

• n raised to the power of r

• r factorial times n factorial

• n plus r factorial

How many possible 4-digit PIN codes can be generated if digits can be repeated?

• 100

• 10,000

• 1,024

• 1,000

How many possible 5-digit security codes are available if digits can be repeated?

• 1,000

• 10,000

• 1,024

• 100,000