Ans: Correct Option is (C) => P = [tex] \frac{ (3C_1)(4C_1)}{12C_2} [/tex]
Explanation:
According to the definition of probability:
Probability of an Event = (Number of favorable outcomes) / (Total number of possible outcomes or sample space)
or,
P = O / S;
First let us find Total number of Possible Outcomes(S):
[tex]S = (3+4+5)C_2[/tex] = 12[tex]C_2[/tex] (Since a student can choose two electives)
In mathematical terms, you can read S as:"The sample space is equals to the combination of 12 taken 2."
Number of favourable outcomes(O):
O = (3-art-electives)[tex]C_1[/tex] * (4-history-electives)[tex]C_1[/tex]
O = (3[tex]C_1[/tex])(4[tex]C_1[/tex])
In mathematical terms, you can read O as:"The outcome is equal to combination of 3 taken 1 times combination of 4 taken 1."
Hence,
Probability P = O/S
P = [tex] \frac{ (3C_1)(4C_1)}{12C_2}
[/tex]
