43 votes 43 votes $n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\) Combinatory gatecse-2003 combinatory normal + – Kathleen asked Sep 16, 2014 edited Feb 15, 2021 by soujanyareddy13 Kathleen 10.4k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Rupendra Choudhary commented Dec 23, 2017 reply Follow Share similar problems https://gateoverflow.in/21007/tifr2012-a-8 https://gateoverflow.in/18496/tifr2010-a-18 8 votes 8 votes ShamikBanerjee commented Apr 16, 2019 reply Follow Share The condition of no one coming is hard to see here. 7 votes 7 votes sayan chowdhury commented Nov 19, 2022 reply Follow Share What type of a party is that !! 2 votes 2 votes Please log in or register to add a comment.
0 votes 0 votes We can also think in terms of boolean inputs. Husband Wife Condition 0 0 both don’t come 👍 0 1 wife without husband 👍 1 0 husband cannot come by himself 👎 1 1 both come together 👍 Thus 3 valid cases! Answer is 3^n. OnewayShruti answered Apr 6, 2021 OnewayShruti comment Share Follow See all 0 reply Please log in or register to add a comment.