Permutation and Combination is one of the one of the most important topic to cover for almost all competitive exams such as MBA Entrance Tests- CAT, GMAT,CMAT,MAT,XAT and the Bank Exams - IBPS PO, IBPS Clerk, IBPS RRB, IBPS SO, SBI BANK PO, and of course SSC Exams.
Our Previous Post FINDING THE UNIT DIGITS- MATHS SHORTCUTS
Many of the books and teachers might have suggested you to solve the permutation and combination problems by applying the following formula.
Believe me or not but its the fact that most of the mistakes occur due to applying this formula while solving the permutation and combination problems. I strongly say that if you have ever felt difficulty in applying the above formula then don’t use it at all.
Instead use the two basic concepts while solving the problem of Permutation and combination. These two concepts are-
Take an example, say you have been asked to find the number of ways in which you can arrange the three letters A, B and C.
Now, there is an important thing to kept in mind before solving this permutation and combination problem. It is whether in the given problem repetition is allowed or not?
Repetition Not Allowed means any given object can not be used more than once in an arrangement.
Repetition Allowed means any given objects can be used as many times as possible to make an arrangement.
Now, we solve the problem when repetition is not allowed,
In first place we can write either A or B or C. it means at first place of possible arrangements there are 3 ways to fill the first place. So we write it as
3 * ---- * -----
Since one letter is already used so now we have only two letters to use means there are only two possible way to fill the second place of the possible arrangement. So we write it as
3 * 2 * -----
At last, we are left with only one un-used letter, it means we can fill the last place in only one way. So we write it as
3* 2* 1 = 6 ways Ans.
How to solve the above problem when repetition is allowed?
In all the places i.e; first place, second place and third place, we can write either A or B or C. It means to fill each place in 3 ways. So we write it as;
3 * 3 * 3 = 27 ways Ans.
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Our Previous Post FINDING THE UNIT DIGITS- MATHS SHORTCUTS
Many of the books and teachers might have suggested you to solve the permutation and combination problems by applying the following formula.
Believe me or not but its the fact that most of the mistakes occur due to applying this formula while solving the permutation and combination problems. I strongly say that if you have ever felt difficulty in applying the above formula then don’t use it at all.
Instead use the two basic concepts while solving the problem of Permutation and combination. These two concepts are-
- Fundamental rule of multiplication, and
- Fundamental rule of Addition.
What is Permutation?
In Simplest words, permutation means ordering or arrangement of the given objects.Take an example, say you have been asked to find the number of ways in which you can arrange the three letters A, B and C.
Now, there is an important thing to kept in mind before solving this permutation and combination problem. It is whether in the given problem repetition is allowed or not?
Repetition Not Allowed means any given object can not be used more than once in an arrangement.
Repetition Allowed means any given objects can be used as many times as possible to make an arrangement.
Now, we solve the problem when repetition is not allowed,
In first place we can write either A or B or C. it means at first place of possible arrangements there are 3 ways to fill the first place. So we write it as
3 * ---- * -----
Since one letter is already used so now we have only two letters to use means there are only two possible way to fill the second place of the possible arrangement. So we write it as
3 * 2 * -----
At last, we are left with only one un-used letter, it means we can fill the last place in only one way. So we write it as
3* 2* 1 = 6 ways Ans.
How to solve the above problem when repetition is allowed?
In all the places i.e; first place, second place and third place, we can write either A or B or C. It means to fill each place in 3 ways. So we write it as;
3 * 3 * 3 = 27 ways Ans.
