If 5 Americans, 4 French people, and 2 British people are to be seated in a row,
ID: 3239154 • Letter: I
Question
If 5 Americans, 4 French people, and 2 British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other? The World Series in baseball continues until either the American League team or the National League team wins four games. How many different orders are possible (e.g., ANNAAA means the American League team wins in six games) if the series goes six games? A student is to answer 8 out of 12 questions in an examination. How many choices does the student have? How many if the student must answer at least 4 of the first 6 questions? A committee of 7 people is to be chosen from a group consisting of 8 men and 9 women. If the committee must consist of at least 2 women and at least 3 men, how many different committees are possible?Explanation / Answer
1 ans) ) 5 americans can be seated in 5! ways
4 french people can be seated in 4! ways
2 british people can be seated in 2! ways
three groups can be arranged in 3 ! ways
total number of required arrangements = 5!*4!*2!*3!= 34560
2)
Let's assume A wins, then double the result.
Okay, so how many ways can A win? A must win the lastgame, but the other games are up for grabs, as long as A wins 3 ofthem. So for question
A wins last game and 3 of first 5. 5 C 3= 5!/(3!(5-3)!) = 10. double it for 20.
3)
Student answered exactly 4 questions out of the first 6
This can be done in 6C4 ways
nCr is the combination of r objects taken out of n, and is defined as
nCr=n!/(r!(n-r)!)
therfore 6!/(4!(6-4)!)= 15
The remaining 4 questions are to be chosen from the remainder, namely 6 questions, in 6 C 4ways =
6!/(4!(6-4)!)= 15
Total =15+15=30
4)
Possible ways are :
( 3 women, 3 men) no. of ways = 9C3 * 8C3 = 84 * 56 = 4704
and
(2 women, 4 men) no. of ways = 9C2 * 8C4 = 36* 70=2520
total no. of possible ways = 4704+2520=7224