Question

Suzy randomly picks marbles form a bag containing 13 identical marbles. how many possible outcomes are there of she selects 10 marbles?

Answer 1

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:

$^nC_r=\frac{n!}{r!(n-r)!}$

here,n=13 and r=10 on substituting the values in the formula we get:

$^13C_{10}=\frac{13!}{10!(13-10)!}$

$^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}$

$\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}$

$\Rightarrow 286$

So, there are 286 possible outcomes.

Answer 2

Possible number of outcome that she can select $10$ marbles from $13$ identical marbles are $\boxed{286}$.

Further explanation:

The formula of combination can be expressed as,

$\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}$

Given:

A bag contains $13$ identical marbles.

Calculation:

Suzy randomly picks $10$ marbles from a bag of $13$ identical marble.

The number of possible outcomes that she can select $10$ marbles can be obtained as,

${\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}$

Substitute $13$ for $n$ and $10$ for $r$ in equation ${^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}$ to obtain the possible outcomes that she can select $10$ marbles from $13$ identical marbles.

$\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}$

Hence, possible number of outcome that she can select $10$ marbles from $13$ identical marbles are $\boxed{286}$.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445

2. Learn more about range and domain of the function brainly.com/question/3412497

3. Learn more about profit and loss brainly.com/question/2479097

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.