# Permutations and Combinations IV: Circular and Complex Permutations and Combinations Questions

In this post, we will discuss Smart Tricks to solve Circular and Complex Permutations and Combinations Questions for Bank Exams.

Permutations and Combinations Questions carry 1-5 marks in bank exams. These marks can be easily scored with the use of permutations and combinations formulas. Permutations are the different ways in which arrangements can be made. Permutations and combinations questions are complicated and often many candidates tend to skip them in bank exams. Especially problems on circular permutations are difficult. But one can solve them easily if they understand the right usage of formulas.

In this post, we have discussed permutations and combinations questions that are based on circular permutations and few complex permutations and combinations questions. Before, we move on to complex permutations and combinations questions, a quick review of the topic and important permutations and combinations formulas will be helpful.
Circular based permutations and combinations questions

The number of Circular Permutation of ‘n’ different objects taken all the time round a circle is given as

(n – 1)!

The number of circular permutation of ‘n’ different objects, all taken at a time, around a circle, (where a particular arrangement in clockwise direction is considered same as a similar arrangement in anti clock direction) is given as

Example 1: Permutations and Combinations Questions

Question: In how many ways can 6 people be seated around a circular table for dinner?
Solution:
Step 1:
Since the people are seated around the circular table we take,
(n-1)!
Here, n = 6

Step 2:
(6 – 1)! = 5! = 120

Therefore, 6 people can sit in 120 ways around a circular table.

Example 2: Permutations and Combinations Questions

Question: How many different garlands can be made using 12 flowers of different colours?
Solution:
Step 1:
The garland can be made in anti-clockwise and clockwise direction. As clockwise and anti-clockwise direction is considered to be the same, we take,

½ (n -1)!

Here n = 12

Step 2:
½ (12 – 1)! =
11!/ 2

Therefore, In 11!/ 2 ways can be found to make garlands from 12 different coloured flowers.
Complex Permutations and Combinations Questions

Example 1: Permutations and Combinations Questions

Question: Eight boys participated in each of the 5 different competitions. In how many different ways can the winner prize be given for all the competitions?

Solution:

Step 1: There are 5 different competitions in which each of these boys can participate and they can participate in all the competitions in order to win a prize.
Hence,
The prizes can be given in 8ways.

Therefore, there are 8ways in which these prizes can be distributed.

Example 2: Permutations and Combinations Questions

Question: In how many ways can the top 3 ranks be awarded for a particular exam/competition involving 12 participants?

Solution :
Step 1: There are 12 participants and 3 ranks, hence if a person secures the first rank then he cannot get the second rank, Likewise, if a person secures the second rank he cannot secure the third rank.

So, 12 x 11 x 10 = 1320 ways.

Therefore, there are 1230 ways in which the top 3 ranks can be awarded.

Permutation and Combinations Questions for Practice

Question: If all possible four digit numbers are formed using the digits 3, 4, 5, 6 without repetition and arranged in ascending order of magnitude then find the position of the number 5463?

(1)  14                (2)22                  (3) 16                (4)19                  (5) None of these

Question: A dance group is such that the number of ways of selecting 5 persons is same as the number of ways of selecting 7 persons. In how many ways can 9 persons be selected from this group?
(1)  180              (2)220              (3) 200              (4)190                (5) None of these