Respuesta :
Answer:
286 possible outcomes.
Step-by-step explanation:
We have been given total 13 identical marbles
We need to select 10 out of 13
We will use combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
here,n=13 and r=10 on substituting the values in the formula we get:
[tex]^13C_{10}=\frac{13!}{10!(13-10)!}[/tex]
[tex]^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}[/tex]
[tex]\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}[/tex]
[tex]\Rightarrow 286[/tex]
So, there are 286 possible outcomes.
Possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
Further explanation:
The formula of combination can be expressed as,
[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]
Given:
A bag contains [tex]13[/tex] identical marbles.
Calculation:
Suzy randomly picks [tex]10[/tex] marbles from a bag of [tex]13[/tex] identical marble.
The number of possible outcomes that she can select [tex]10[/tex] marbles can be obtained as,
[tex]{\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}[/tex]
Substitute [tex]13[/tex] for [tex]n[/tex] and [tex]10[/tex] for [tex]r[/tex] in equation [tex]{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex] to obtain the possible outcomes that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles.
[tex]\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}[/tex]
Hence, possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Combination
Keywords: Suzy, picks, marbles, 13 identical marbles, 10 marbles, possible, outcomes, select, combination, randomly picks, a bag contains 13 marbles.
