Robert Bosch Permutation and Combinations Quiz 2

Total cards = 52
Drawn cards(Heart) = 2
Present total cards = total cards-drawn cards =52-2=50
Remaining Card 13-2 = 11
Probability = 11/50

Probability = \frac{(\frac{3}{5} * \frac{5}{8})}{([\frac{3}{5} * \frac{5}{8}] + [\frac{2}{5} * \frac{1}{3}]) } = \frac{45}{61}

P(A) = \frac{^{20}C_{2}}{^{30}C_{2}}, P(B) = \frac{^{22}C_{2}}{^{30}C_{2}}
P(A \cap B) = \frac{^{15}C_{2}}{^{30}C_{2}}
P( A \cup B ) = P(A) + P(B) – P(A \cap B)
=> ( \frac{^{20}C_{2}}{^{30}C_{2}})+( \frac{^{22}C_{2}}{^{30}C_{2}})-( \frac{^{15}C_{2}}{^{30}C_{2}}) = \frac{316}{435}

Five persons is to be chosen from a group of 10 people = ^{10}C_{5} = 252
Couple Serve together = ^{8}C_{3}* ^{2}C_{2} = 56
Couple does not serve = ^{8}C_{5} = 56
Probability = \frac{102}{252} = \frac{51}{126}

Man only = ^{8}C_{2}= 14
Probability of selecting no woman = \frac{14}{91}
Probability of selecting atleast one woman = 1 – \frac{14}{91}= \frac{77}{91}

Total probability = ^{6}C_{2} = 15
Probability that one is Banana and another one is orange = ^{3}C_{1} *^{3}C_{1} = 9
probability = \frac{9}{15} = \frac{3}{5}

 

Total Balls = 15
Probability = \frac{^{6}C_{3}}{^{15}C_{3}} = \frac{4}{91}

Total Balls = 15
Probability = ^{4}C_{2} * \frac{^{3}C_{1}}{^{15}C_{3}} = \frac{18}{455}

Total Balls = 15
Probability = \frac{^{11}C_{4}}{^{15}C_{4}}= \frac{22}{91}
One is black = 1 – \frac{22}{91} = \frac{69}{91}

 

Probability both are Pink = \frac{1}{^{15}C_{2}}
Probability both are Green = \frac{3}{^{15}C_{2}}
Required Probability = \frac{4}{^{15}C_{2}} = \frac{4}{105}