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slava [35]
3 years ago
14

A Poker club has 10 members. A president and a vice-president are to be selected. In how many ways can this be done if everyone

is eligible?
Mathematics
1 answer:
Nesterboy [21]3 years ago
7 0

Answer:

90 different ways

Step-by-step explanation:

We have a total of 10 members, and we want to find how many groups of 2 members we can have, where the order of each member in the group of 2 is important, so we have a permutation problem.

To solve this problem, we need to calculate a permutation of 10 choose 2.

The formula for a permutation of n choose p is:

P(n, p) = n! / (n - p)!

So we have:

P(10, 2) = 10! / (10 - 2)!

P(10, 2) = 10! / 8!

P(10, 2) = 10*9 = 90

So there are 90 different ways of choosing a president and a vice-president.

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cricket20 [7]

Answer: P(odd) = 0.499

Step-by-step explanation:

Given:

Total number of people = 20

Number of men = 12

Number of women = 8

Number of jury to be selected = 6

For the jury to have an odd number of women. it must have either of the three.

1. 1 woman , 5 men

2. 3 women, 3 men

3. 5 women, 1 man

The total possible ways of selecting the 6 people jury is;

N = 20C6 = 20!/6!(20-6)!

N = 38760

The possible ways of selecting;

Case 1 : 1 woman, 5 men

N1 = 8C1 × 12C5

N1 = 8 × 792 = 6336

Case 2 : 3 women , 3 men

N2 = 8C3 × 12C3

N2 = 12320

Case 3 : 5 women, 1 man

N3 = 8C5 × 12C1

N3 = 672

P(Odd) = (N1+N2+N3)/N

P(odd) = (6336+12320+672)/38760

P(odd) = 19328/38760

P(odd) = 0.499

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