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x, y and z are positive integers. How many different ordered groups of

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Bunuel
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x, y and z are positive integers. How many different ordered groups of [#permalink] New post   23 Jun 2022, 08:30
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x, y and z are positive integers. How many different ordered groups of {x, y, z) are possible so that x + y + z = 5?

A. 3
B. 4
C. 5
D. 6
E. 8
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D
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Re: x, y and z are positive integers. How many different ordered groups of [#permalink] New post   23 Jun 2022, 08:35
Bunuel wrote:
x, y and z are positive integers. How many different ordered groups of {x, y, z) are possible so that x + y + z = 5?

A. 3
B. 4
C. 5
D. 6
E. 8


possible pairs of ( x,y,z) such that x+y+z=5
(1,1,3) ; ( 1,2,2)
1,1,3 can be arranged in 3!/2! ; 3 ways
so can be ( 1,2,2 ) 3 ways
total ways 6 option D
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x, y and z are positive integers. How many different ordered groups of [#permalink] New post   Updated on: 23 Jun 2022, 08:37
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Permutation with repetition where n = k
n = number os elements
k = number of places
n = k the order matters
There’s no repetition
n! In the numerator and the number of repetitions! in the denominator
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Originally posted by MBAHOUSE on 23 Jun 2022, 08:37.
Last edited by MBAHOUSE on 23 Jun 2022, 08:37, edited 1 time in total.
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Re: x, y and z are positive integers. How many different ordered groups of [#permalink] New post   23 Jun 2022, 08:37
There are only two possibilities: 1+1+3 = 5 ,or, 1+2+2=5.
Since, we require ordered pairs, total number of ordered pairs of (1,1,3) & (1,2,2) = \(\frac{3!}{2} + \frac{3!}{2} = 3+3 = 6\). Option (D)

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Re: x, y and z are positive integers. How many different ordered groups of [#permalink]
23 Jun 2022, 08:37
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