A jar contains 6 Magenta balls, 3 Tan balls, 5 Gray balls

Both balls are tan = 3/21 × 2/20 = 1/70

Ok. But what about this one:
a-bag-has-4-blue-3-yellow-and-2-green-balls-the-balls-of-139818.html

In this example, the number of ways of choosing any one out of 3 Yellow balls = 1+1+1+1 (no ball is chosen) instead of (3C0=1)+(3C1=3)+(3C2=3)+(3C3=1)=8 ways

Can you please explain the difference between these two questions?

Eva,
Sorry to open this old thread. But, in this post : math-combinatorics-87345.html , the poster has mentioned that "Number of ways to pick 0 or more objects from n identical objects = n + 1" -- Hence, the number of ways to pick 2 balls out of say 5 identical balls must NOT be 5C2 -- Correct? Please help me.

thanks

If it is not stated, we should assume without replacement,
Therefore: 3/21 x 2/20 = 1/70

Answer A

[/quote]


Eva,
Sorry to open this old thread. But, in this post : math-combinatorics-87345.html , the poster has mentioned that "Number of ways to pick 0 or more objects from n identical objects = n + 1" -- Hence, the number of ways to pick 2 balls out of say 5 identical balls must NOT be 5C2 -- Correct? Please help me.

thanks[/quote]

The wording "Number of ways to pick 0 or more objects from n identical objects = n + 1" is not clear.
It is meant that from n identical objects, we can choose none (which is 0), 1, 2,..., or all n objects - therefore we have n+1 choices.
For example, if we have 5 identical balls, we can choose 0, 1, 2, 3, 4, or 5 balls. We have a total of 5 + 1 choices.

Once we made up our mind how many balls we want to choose, say 2, then the number of possibilities to choose them is 5C2 = 5*4/2.
Because, for the first ball 5 possibilities, for the second 4 possibilities, and then we have to divide by 2!, because the balls are identical, order doesn't matter (I would say it is meaningless, red is red, so why should I care which red I picked first?).[/quote]

Hi,

i have a small doubt in this.

This example of 5 balls and pick up 2 ball can be written as like this also right
Probablity to take first ball is : 2/5
Probablity to take second ball: 1/4
so independent event = 2/5* 1/4= 1/10
which is reciprocal of wat u got. . is this correct answer.? i am trying to understand this in probablity ways/ pleas healp me


Thanks,
Rrsnathan

Probability = \(\frac{Desired Outcomes}{Total Outcomes}\)

Desired Outcomes = Number of ways of choosing 2 tan balls from 3 Tan balls = 3C2

Total Outcomes = Number of ways of choosing any 2 balls from 21 balls = 21C2

Thus Probability = \(\frac{3C2}{21C2}\) = \(\frac{1}{70}\)

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