Question

In how many ways can 3 students from a class of 10 be chosen for a field trip?

Answer #1

These kind of questions have a basic thumb rule:

Whenever you have to choose and repetition is not allowed,

as in, in this case one student can not be selected more than once

also, the order of selection does not matter, that means if any three students A,B and C are selected in whatever order be ABC, ACB, BAC, BCA, CAB, CBA are counted as one kind of selection only

These kind of problem can directly be solved using Combination

Here, we can use 10C3 where 10C3 is (10 factorial / ( 3 factorial * 7 factorial ))

to calculate factorial :

n factorial = n*(n-1)*(n-2)*.....*3*2*1

S, number of ways 3 students can be chosen from a class of 10 = (10*9*8*7*6*5*4*3*2*1 / ((7*6*5*4*3*2*1)*(3*2*1))) = (10*9*8/3*2*1) = 720/6 = 120 ways

There are 11 students in a very small 3rd grade class. In how
many ways can the 11 students be lined up to go out for recess? The
teacher needs to choose two students to serve on the 3rd grade
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A class has 29 students. In how many different ways can four
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There are
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in how many ways can a teacher divide a class of 14
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A group of college students contains 7 seniors and 8
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a) In how many ways can 3 individuals from this group be chosen
for a committee?
b) In how many ways can a president, vice president, and
secretary be chosen from this group?
c) Suppose instead, there are n seniors and m juniors, for some
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1. A 4-digit number is created from the numbers {1,2,3,4,5,6}.
How many ways can the digits be chosen so that the number is more
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2. An applied statistics class contains 30% sophomores, 40%
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In a group of 2 freshmen, 3 Sophomores, and 10 Junior
in how many
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b. the two freshmen must be included?
c. the two freshmen must be excluded?
d. there must be at least 4 juniors?
e.there must be at most 3 sophomores?

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