Question

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i) When thirty persons shake hands with one another, in how many ways is it possible?

II) Three children took part in a racing competition in their school with their respective probabilities to reach the following point being 1/3, 1/5 and 1/4 respectively. What is the probability that at least one of them will finish the race?

Kindly ignore if you don't know the answer. ​

Answer 1

1) 30 people there.

(consider one people as you)

So 29 out of 30

each handshake counts for 2 people so,

$\frac{30}{2} \times 29$

${\cancel{\frac{30}{2}}} \: \: ^{15} \times 29$

$= 15 \times 29 \\ = 435$

2) Let the names of children be x, y and z. The probabilities of the three children to finish the race are 1/3, 1/5 and 1/4 respectively. It may be noted that one reaching the finishing point is independent of other reaching. If P(x), P(y) and P(z) denotes the probabilities.

The probability of at least one of them reaching the finishing point = 1 – P

(none of them finishing the race)

$1 - (\frac{2}{3})( \frac{4}{5})( \frac{3}{4}) \\ \\ = 1 - \frac{24}{60} \\ \\ = \frac{60 - 24}{60} \\ \\ = \frac{36}{60} \\ \\ = \cancel \frac{36}{60} \: ^{ \frac{3}{5} } \\ \\ = \frac{3}{5}$

Hope This Helps You ❤️

Answer 2

Answer:

Elite Member. Simpler: Every one of the 30 people shakes hands with the other 29 people. However, each handshake counts for 2 people: 30(29)/2= 15(29)= 435.