Counting Possible BIJECTIVE Functions Given Constraints

Occasionally Maths Olympiads and College Entrance Tests ask a question along the lines of 'how many possible BIJECTIVE functions are there from set A to set B which satisfy certain constraints?'. Frankly there is no better way to understand how to do these types of questions than simply to attempt as many of them as possible for familiarity and practice.

In this video we answer two such questions, both from recent JEE Main exams, and as we see during the video there is no 'simple formula' which covers them. Each question is different in its own constraint, though there are some similarities which we can take advantage of.

In question 2 at 5:28, even though it is actually a surjective (onto) function question, because the domain and codomain are the same size it is also a bijective function question and thus better dealt with in this video rather than our video on surjective functions with unequal domain and codomain sizes, where the methods used are completely different (see below playlist for our video on counting such surjective functions).

IMPORTANT CORRECTION: At 4:42 the author erred and wrote 33 instead of 18.

Counting is not easy - it is quite difficult not to double count or omit possibilities, so care really needs to be taken. There are certainly overlaps with these types of questions and other types of 'counting'. As such, it may be beneficial to try out some of our other 'Counting' videos in our playlist 'Counting'

For more videos on bijective functions, see our playlist 'Injective (one-to-one), Surjective (onto) and Bijective Functions'

For more videos on JEE Main see our playlist 'JEE Aspirant'

For more videos on functions generally see our playlist 'Functions'

For more videos on Maths Olympiads, see our playlist 'Maths Olympiads'

For more videos on College Entrance Tests see our playlist 'UPCAT and Other CETs'

[bonzobobajob]

I don't understand why this video has so few views... it's a great overview thank u👍