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GATE | GATE-CS-2003 | Question 4

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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)

256
 

(B)

56
 

(C)

30
 

(D)

2
 


Answer: (B)

Explanation:

Suppose you have selected 3 elements from 8 in 8C3 ways, the remaining elements are treated as another array and merging both the arrays gives the sorted array. Here, you can select either 3 or 5. 

=> 8C3 = 8C5 = 8!/(3!5!) = 7*8 = 56 Ways. 
 


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Last Updated : 28 Jun, 2021
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