Question

Six exam papers are to be set in a certain order not to be disclosed. It is discovered that one order has been leaked out. The number of ways that their order can be changed is
A. ${}^6{P_1}$
B. ${}^6{C_1}$
C. 216
D. 719

Answer 1

Hint: Given that six exam papers are to be set in certain order which should not be disclosed and one order has been leaked out. If the number of exam papers is ‘n’, then the number of ways in which those n papers can be arranged irrespective of the order is $n!$. One order is leaked out so the total no. of ways the order can be changed will be one less from $n!$

Complete step-by-step answer:
We are given that 6 exam papers are to be set in a certain order not to be disclosed and one order has been leaked out.
We have to calculate the no. of ways their order can be changed.
Here, the order of the papers is not important. So the no. of ways the 6 papers can be arranged is
 $
 n! \\
 n = 6 \\
 \to 6! = 720ways \\
$
But one way (order) of arranging these 6 papers is already leaked out.
So the final number of ways the order of 6 papers can be changed is $720 - 1 = 719$
So, the correct answer is “Option D”.

Note: A permutation is arranging the objects in order. Combinations are the way of selecting the objects from a group of objects or collection. When the order of the objects does not matter then it should be considered as Combination and when the order matters then it should be considered as Permutation. Do not confuse a permutation with a combination.