In how many ways can 5 people from a group of 6 people be seated aroun

Question

In how many ways can 5 people from a group of 6 people be seated around a circular table

A. 56
B. 80
C. 100
D. 120
E. 144

MayankSingh · Answer

E:144
5 people out of 6 = 6C5=6
And 5 people around a circular table = (5-1)!=24
So total ways = 6x24=144

Posted from my mobile device

Kinshook · Answer

Number of ways = 6C5 * 4! = 144

IMO E

MaartjeZ · Answer

I don't understand why seating 5 people around a circular table is (5-1)! and not 5!. Can anybody explain? Does it have something to do with the table being circular?

ThatDudeKnows · Answer

If we were asking how many ways there are to line the five people up from left to right, we would have left, next-to-left, middle, next-to-right, and right. You'd have five choices to fill the first slot, four to fill the second, three to fill the third, two to fill the fourth, and one to fill the fifth. So, 5*4*3*2*1, which is 5! HOWEVER, we are looking at a circular table. If everyone is seated and just gets up and moves one seat to the left, we don't want to count that as a new arrangement. It's the same arrangement, just rotated one seat to the left. So how do we solve it? Let's say we seat person A and then work to the left, there are now four choices to fill the seat to the left of A, three choices to fill the seat two to the left of A, two choices to fill the seat three to the left of A, and one choice to fill the last seat. So, 4*3*2*1, which is (5-1)!.

Nalapatricia · Answer

In how many ways can 5 people from a group of 6 people be seated around a circular table

First:

Way to select 5 person from 6:
6C5 : 6*5*4*3*2*1/1*5*4*3*2*1 = 6

Ways to arranged 5 person in a round table is (N-1!) = 4! = 24

Total ways to arranged and choose the people = 24*6 = 144
Correct answer:
E. 144

In how many ways can 5 people from a group of 6 people be seated aroun

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In how many ways can 5 people from a group of 6 people be seated aroun

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards