 October 7, 2023
October 7, 2023
October 7, 2023
###### GATE 2003
October 7, 2023
 Question 4

Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?

 A 2 B 30 C 56 D 256
Question 4 Explanation:
A can have sequence of 8 distinct integers which are sorted in ascending order.
→ If we are pick 3 elements from 8 sequence integers then remaining 5 elements are already in ascending order. After merging these elements then it gives A.
→ No. of possibilities of choosing 8 elements from total of 8 = 8C3
= 8!/3!5!
= 8 * 7
= 56
Question 4 Explanation:
A can have sequence of 8 distinct integers which are sorted in ascending order.
→ If we are pick 3 elements from 8 sequence integers then remaining 5 elements are already in ascending order. After merging these elements then it gives A.
→ No. of possibilities of choosing 8 elements from total of 8 = 8C3
= 8!/3!5!
= 8 * 7
= 56