Question

Mahavir was preparing for the FAT exam and enrolled for the PRAC-FAT series of a tutorial which offered 23 PRAC-FAT papers for practice. However, Mahavir decided
to appear for exactly nine out of the 23 PRAC-FAT papers, while skipping the rest. Further, he decided against appearing for any two consecutive papers but did not
want to miss the last paper Find the total number of ways in which Pradip can appear for the PRAC-FATS.​

Answer 1

Answer:

my first answer is pradip can appear for the tests as per his will. how would decision of mahavir affect action of pradip?

(I answered this coz I thought it might be a puzzle)

now

since mahavir will appear in the 23 rd test, he will not appear in 22 nd test.

now from rest 21 papers he would appear in 8 papers so that he does not appear in any two consecutive paper.

we know that total number of ways of selecting r items out of n items so that no two items are consecutive is (n-r+1)Cr ways

hence the required number of ways is

(21-8+1)C8

= 14C8 ways

= (14*13*12*11*10*9)/(1*2*3*4*5*6)

= 3003 ways