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stealth61 [152]
3 years ago
14

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the pro

bability that both students chosen are sophomores? StartFraction (6 C 1) (5 C 1) Over 20 C 2 EndFraction StartFraction (6 P 1) (5 P 1) Over 20 P 2 EndFraction StartFraction (20 C 6) (19 C 5) Over 20 C 2 EndFraction StartFraction (20 P 6) (19 P 5) Over 20 P 2 EndFraction
Mathematics
2 answers:
Elanso [62]3 years ago
7 0

Answer:

<em>Choose the first alternative</em>

\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}

Step-by-step explanation:

<u>Probabilities</u>

The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions (N_s) and the total number of possible choices (N_t), i.e.

\displaystyle P=\frac{N_s}{N_t}

There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total

We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.

To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5

_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C} \text{ ways to do it}

The total number of possible choices is

_{2}^{20}\textrm{C} \text{ ways to do it}

The probability is then

\boxed{\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}}

Choose the first alternative

Verdich [7]3 years ago
3 0

Answer:

(6C1)(5C1)/20C2

Step-by-step explanation:

Was right on egde

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