###### NIC-NIELIT Scientist-B 2020

October 7, 2023###### GATE 2003

October 7, 2023# GATE 2003

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?

2 | |

30 | |

56 | |

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 =

= 8!/3!5!

= 8 * 7

= 56

→ 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 =

^{8}C_{3}= 8!/3!5!

= 8 * 7

= 56

Correct Answer: C

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 =

= 8!/3!5!

= 8 * 7

= 56

→ 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 =

^{8}C_{3}= 8!/3!5!

= 8 * 7

= 56

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