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04 Dec 2022, 08:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:26) correct
42%
(01:25)
wrong
based on 336
sessions
History
Date
Time
Result
Not Attempted Yet
In how many different ways can a group of six students be equally distributed into three classes: physics, mathematics and history ?
(A) 6
(B) 15
(C) 20
(D) 45
(E) 90
(A) 6
(B) 15
(C) 20
(D) 45
(E) 90
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04 Dec 2022, 09:49
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Bunuel
How would you solve if you did not know the formula?There are 6 students, we can select two students for physics class in 6C2 ways.
As two students have been selected we have 4 students left, two student can be selected for mathematics class in 4C2 ways
As four students have been selected we have two students who can be selected for history class in 2C2 ways
Total = 6C2 * 4C2 * 2C2 = \(\frac{6*5 }{ 2*1} * \frac{4*3}{2*1} * \frac{2 * 1}{2*1\\
}\) = \(\frac{6! }{ (2!)^3}\)
Total = 90 ways
04 Dec 2022, 09:27
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Bunuel
The groups are distinct. The number of ways of arranging "n" people into "y" distinct groups consisting of "x" members in each group is given by
\(\frac{n ! }{ (x!)^y} \)
n = y * x
In this case n = 6
y = 3
x = 2
Number of ways = \(\frac{6! }{ (2!)^3 }\) = 90
Option E
