Question
Out of 10 men, 3 are wearing red caps, 4 are wearing
green caps, and the remaining men are wearing orange caps. They are to be seated in a linear row. If the number of ways they can be arranged such that no more than three men wearing green caps sit next to each other is 'q', find the sum of the squares of each digit of 'q'.Solution
ATQ,
Total number of ways in which all of them can seat = 10! = 36,28,800 Number of ways in which all 4 men wearing green cap sit next to each other:
= 7! X 4! = 1,20,960
'q' = 36,28,800 - 1,20,960 = 35,07,840
Required sum = 3² + 5² + 0² + 7² + 8² + 4² + 0²
= 9 + 25 + 0 + 49 + 64 + 16 + 0 = 163
Which company won four gold awards at the Olive Crown Awards 2025?
The objective of Bima Vahak continues to be a women-centric, dedicated distribution channel that will ensure accessibility and availability of insurance...
- Which dynasty founded the Vijayanagar Empire?
Who authored the book *‘Divorce and Democracy: A History of Personal Law in Post-Independence India’*?Â
From which site was India’s first satellite Aryabhata launched?
Who was elected as the President of the 68th General Conference of the International Atomic Energy Agency (IAEA) in September 2024?
Who, in a historic achievement, has become the first female medical officer in the Indian Army to be stationed at Siachen, the highest battlefield in th...
- Who holds the distinction of being the first judge against whom impeachment proceedings were initiated in independent India?
Who is the chairperson of the working group for the revision of WPI base year and transition to PPI?
"Exercise Sea Dragon 2026" is a US-led multinational exercise. In which region was it conducted in March 2026?
