Permutation Quiz

What is a permutation?

• An arrangement of objects in a definite order

• A selection of objects where order does not matter

• A method of calculating probabilities

• A type of mathematical function

Answer explanation

A permutation refers to an arrangement of objects in a specific order. This distinguishes it from combinations, where the order of selection does not matter. Therefore, the correct choice is 'An arrangement of objects in a definite order'.

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

• n!/(n-r)!

• n!/(r!(n-r)!)

• n^r

• n! + r!

Answer explanation

The formula for permutations of n objects taken r at a time is given by n!/(n-r)!. This represents the number of ways to arrange r objects from a total of n, making it the correct choice.

In how many ways can 3rd and 4th positions be awarded to 10 members?

• 90

• 720

• 60

• 100

Answer explanation

To award the 3rd and 4th positions to 10 members, we choose 2 members from 10 and arrange them. This is calculated as 10P2 = 10!/(10-2)! = 10*9 = 90. Thus, the correct answer is 90.

What does nPr represent?

• The factorial of n

• The sum of n and r

• The number of permutations of n objects taken r at a time

• The number of combinations of n objects taken r at a time

Answer explanation

nPr represents the number of permutations of n objects taken r at a time, which calculates how many different ways you can arrange r objects from a set of n distinct objects.

Which of the following is a type of permutation?

• Permutation of n different objects

• Sum of n and r

• Combination of n different objects

• Factorial of n

Answer explanation

The correct choice, 'Permutation of n different objects', refers to the arrangement of n distinct items in a specific order, which is a fundamental concept in permutations. The other options do not represent types of permutations.

What is the permutation formula when repetition is allowed?

• n^r

• n!/(n-r)!

• n!/(r!(n-r)!)

• n + r

Answer explanation

The permutation formula when repetition is allowed is n^r, where n is the number of options and r is the number of selections. This means each selection can be any of the n options, leading to n multiplied by itself r times.

What is the difference between permutation and combination?

• Order matters in permutation but not in combination

• Combination is always greater than permutation

• Permutation is used only for numbers

• Both have the same formula

Answer explanation

In permutations, the arrangement of items is important, meaning different orders count as different permutations. In combinations, the order does not matter, so different arrangements of the same items are considered the same combination.

How many ways can 6 children be arranged in a line if two particular children must be together?

• 240

• 120

• 720

• 480

Answer explanation

Treat the two particular children as one unit. This gives us 5 units to arrange (4 children + 1 unit). The arrangements of these 5 units is 5! = 120. The two children can switch places, giving 120 x 2 = 240 ways. Thus, the answer is 240.

What is the fundamental counting principle?

• The product of all combinations

• The average of n and r

• The sum of all permutations

• If one operation can be performed in m ways and another in n ways, then together they can be performed in m x n ways

Answer explanation

The fundamental counting principle states that if one operation can be performed in m ways and another in n ways, then the total number of ways to perform both operations is m x n. This is the correct choice.

In how many ways can 3 elements be selected from a set of 5 elements?

• 10

• 20

• 15

• 5

Answer explanation

To select 3 elements from a set of 5, use the combination formula C(n, r) = n! / (r!(n-r)!). Here, C(5, 3) = 5! / (3!2!) = 10. Thus, the correct answer is 10.