Question 1

A construction company based on Muscat must send a project team (4 people) to work on a new job site. If the company has 16 available staff, how many possible project teams are there?&#10;A) 1820&#10;B) 1868&#10;C) 1892&#10;D) 1902

Accepted Answer

The number of possible project teams can be calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items (in this case, staff members), and k is the number of items to choose (in this case, team members). Here, n=16 and k=4, so C(16, 4) = 16! / [4!(16-4)!] = 1820.

Question 2

Calculate&#10;A) 18&#10;B) 22&#10;C) 26&#10;D) 30

Accepted Answer

30

Question 3

What is the correct value of 5! ?&#10;A) 110&#10;B) 120&#10;C) 130&#10;D) 14

Accepted Answer

5 factorial (5!) means 5 * 4 * 3 * 2 * 1, which equals 120.

Question 4

Calculate the number of permutations of 3 items from a set of 6 items.&#10;A) 80&#10;B) 100&#10;C) 120&#10;D) 140

Accepted Answer

The number of permutations of 3 items from a set of 6 items is calculated using the formula P(n, r) = n! / (n-r)!, where n is the total number of items and r is the number of items to be arranged. Here, n=6 and r=3, so P(6, 3) = 6! / (6-3)! = 6! / 3! = (6*5*4*3*2*1) / (3*2*1) = 6*5*4 = 120.

Question 5

An accounting firm in Iran has won two new contracts. Each contract needs one accountant to work on it, but the same accountant cannot undertake both. Should the manager be concerned about combinations or permutations of staff that might undertake this work?

A) Combinations
B) Permutations
C) Both are important
D) Neither is important

Accepted Answer

The manager should be concerned about permutations because the order in which the accountants are assigned to the contracts matters. Each contract is distinct, so assigning Accountant A to Contract 1 and Accountant B to Contract 2 is different from assigning Accountant B to Contract 1 and Accountant A to Contract 2.

Question 6

A delivery company must send two of its 10 vans to pick up an order from a customer in Abu Dhabi. Should the transport manager be concerned about combinations or permutations of vans that could be used?

A) Combinations
B) Permutations
C) Both are important
D) Neither is important

Accepted Answer

The order in which the vans are sent does not matter; what matters is which two vans are chosen out of the ten. This is a matter of combinations, not permutations.

Question 7

A bakery conducts checks each day to make sure that its scales are weighing accurately. It checks once per day and there is a chance that the scales need adjusting of 0.15 each day. If it checks 30 times in a month, what are the chances of the scales needing adjusting on precisely 5 occasions (3 decimal places)?

A) 0.156
B) 0.166
C) 0.176
D) 0.186

Accepted Answer

The answer of A bakery conducts checks each day to...

Question 8

Which of the following options is the BEST definition of a permutation?&#10;A) A selection of distinct elements from a set&#10;B) The number of elements in a set&#10;C) A selection of distinct elements from a set, arranged in a particular way&#10;D) All the elements from a set

Accepted Answer

A permutation refers to the arrangement of all or part of a set of objects, with regard to the order of the arrangement. Option C captures this definition accurately by mentioning both the selection of distinct elements and their arrangement.

Question 9

How many combinations of 2 vans can be made from a fleet of 10?&#10;A) 42&#10;B) 45&#10;C) 48&#10;D) 51

Accepted Answer

The number of combinations of 2 vans from a fleet of 10 is calculated using the combination formula, which is n! / [r!(n-r)!], where n is the total number of items (10 vans) and r is the number of items to choose (2 vans). So, it's 10! / [2!(10-2)!] = 10! / (2!8!) = (10*9) / (2*1) = 45.

Question 10

Which of the following options is the BEST definition of a combination?&#10;A) A selection of distinct elements from a set&#10;B) The number of elements in a set&#10;C) A selection of distinct elements from a set, arranged in a particular way&#10;D) All the elements from a set

Accepted Answer

A combination refers to the selection of distinct elements from a set without regard to the order in which they are selected. This distinguishes it from a permutation, which does consider the order of selection.

Deck 32: Combinations and Permutations