11 beads: 7 red , 4 white
[tex]probability = \frac{the \: desired \: outcome}{all \: possible \: outcomes} [/tex]
we calculate the desired outcome using combinations of 11 beads. we know that we can select "r" beads from "n" beads in this way:
[tex] \binom{n}{r} = \frac{n!}{r!(n - r)!} [/tex]
where:
[tex]n! = n \times (n - 1) \times ... \times 3 \times 2 \times 1[/tex]
so the probability is:
[tex]p = \frac{ \binom{7}{1} \times \binom{4}{1} }{ \binom{11}{2} } = \frac{7 \times 4}{55} = \frac{28}{55} [/tex]
