Combinations and Permutations Concepts

The video tutorial explains permutations and combinations, starting with an example of seating 5 people in 3 chairs. It derives the formula for permutations as n factorial over n minus k factorial. The video then introduces combinations, explaining how they differ from permutations by not considering order. It calculates combinations by dividing permutations by the factorial of the number of positions. The tutorial concludes with the general formula for combinations, known as the binomial coefficient, which is n factorial over r factorial times n minus r factorial.

How many different ways can 5 people be seated in 3 chairs if the order matters?

• 120

• 10

• 60

• 15

What is the general formula for calculating permutations of n items taken k at a time?

• n factorial times k factorial

• n factorial divided by (n-k) factorial

• n factorial divided by k factorial

• k factorial divided by n factorial

In the context of permutations, what does 'n factorial' represent?

• The difference of all numbers from 1 to n

• The product of all numbers from 1 to n

• The division of all numbers from 1 to n

• The sum of all numbers from 1 to n

What distinguishes a combination from a permutation?

• Combinations consider order, permutations do not

• Permutations consider order, combinations do not

• Neither consider order

• Both consider order

How do you calculate the number of combinations of n items taken r at a time?

• Divide the number of permutations by r factorial

• Multiply the number of permutations by r factorial

• Add the number of permutations to r factorial

• Subtract r factorial from the number of permutations

If you have 5 people, how many different groups of 3 can be formed?

• 15

• 5

• 10

• 20

What is the value of 3 factorial?

• 9

• 6

• 12

• 3

How many permutations are there for arranging 3 people in 3 seats?

• 9

• 12

• 3

• 6

What is the binomial coefficient often used for?

• Solving linear equations

• Polynomial expansion

• Calculating factorials

• Calculating permutations

What is the formula for calculating the number of combinations?

• n factorial divided by (r factorial times (n-r) factorial)

• n factorial times r factorial

• r factorial divided by n factorial

• n factorial divided by r factorial