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In a basket there are 10 mangoes, 5 apples, 5 guavas and 6 oranges. If two fruits are drawn at random one after another without replacement, then find the probability of the fruits to be of different type.

Solution: total fruits = 26

1st Mango & 2nd Apple =

\frac{10}{26} \cdot \frac{5}{25}

\frac{50}{650}

1st Mango & 2nd Guava =

\frac{10}{26} \cdot \frac{5}{25}

\frac{50}{650}

1st Mango & 2nd Orange =

\frac{10}{26} \cdot \frac{6}{25}

\frac{60}{650}

1st Apple & 2nd Guava =

\frac{5}{26} \cdot \frac{5}{25}

\frac{25}{650}

1st Apple & 2nd Orange =

\frac{5}{26} \cdot \frac{6}{25}

\frac{30}{650}

1st Apple & 2nd Mango =

\frac{5}{26} \cdot \frac{10}{25}

\frac{50}{650}

1st Guava & 2nd Orange =

\frac{5}{26} \cdot \frac{6}{25}

\frac{30}{650}

1st Guava & 2nd Mango =

\frac{5}{26} \cdot \frac{10}{25}

\frac{50}{650}

1st Guava & 2nd Apple =

\frac{5}{26} \cdot \frac{5}{25}

\frac{25}{650}

1st Orange & 2nd Mango =

\frac{60}{650}

1st Orange & 2nd Apple =

\frac{30}{650}

1st Orange & 2nd Guava =

\frac{30}{650}

Probability of being different fruits =

\frac{50}{650} + \frac{50}{650} + \frac{60}{650} + \frac{25}{650} + \frac{30}{650} + \frac{50}{650} + \frac{30}{650} + \frac{50}{650} + \frac{25}{650}

\frac{60}{650} + \frac{30}{650} + \frac{30}{650}

\frac{490}{650}

\frac{49}{65}