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I have attempted to set these up but want to make sure I'm on the right track. Any help is appreciated!

Dante can only invite 8 people to his birthday, but has 13 friends he’d like to invite. Eight of his friends are boys and five are girls. If Dante randomly selects 8 people, determine the probability for each scenario.

  1. Dante does not invite any girls
    $\binom{13}{8}$ Randomly selecting 8 people
    $\binom{8}{8}$ not girls
    = $\binom{13}{8}$ $\binom{8}{8}$

  2. Dante invites an equal number of boys and girls
    This would mean out of the 8 people, 4 need to be boys and 4 girls.
    $\binom{13}{8}$ Selection
    $\binom{8}{4}$ boys
    $\binom{5}{4}$ girls
    = $\binom{13}{8}$ ? $\binom{8}{4}$ * $\binom{5}{4}$


marked as duplicate by lulu, Parcly Taxel, Joel Reyes Noche, hardmath, user223391 Oct 28 '16 at 16:50

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  • $\begingroup$ Note that a probability is a value between zero and one. You are counting outcomes, which is a good start, but the probability is obtained as a ratio of the favorable outcomes to all possible outcomes. $\endgroup$ – hardmath Oct 28 '16 at 14:45

Basically, you need to put the total number of possibilities in denumerator and the number of desired possibilities in the numerator.

  1. $$\frac{\binom{8}{8}}{\binom{13}{8}}$$

  2. $$\frac{\binom{8}{4}\binom{5}{4}}{\binom{13}{8}}$$


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