Question

A box contains 7 red, 6 white and 4 blue balls. 3 balls are randomly.If
the red coloured ball is not taken, then the number of selections is​

Answer 1

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You have 17 balls in total. Of these, 7 are red, and the other 10 are not. You wish to know how many ways you can select 3 balls such that none of them is red.

This means you are selecting 3 balls from the 10 non-red balls.

This can be done in  (103)=120  ways.

It’s interesting to note that this answer in no way depends on the number or red balls. There could be a million read balls, and the answer wouldn’t change.

Now if you wanted the probability that you’d pick 3 non-red balls, you have to divide the answer given above by the total ways of picking any 3 balls. and that definitely depends on the number of red balls.

The total number of ways of picking any 3 balls is  (173)=680 .

To get the probability of drawing no red balls, we just divide 120/680 to get about 18%.

Answer 2

Answer:

The required probability is $3/17$.

Step-by-step explanation:

It is given that a box contains $7$ red, $6$ white and $4$ blue balls.

Three balls are randomly taken.

If the red colored ball is not taken, then we need to determine number of selections.

Non red balls are $10$.

Selecting $3$ balls from the $10$ non-red balls is done in 10$c_{3}$$=120$ ways.

Favorable cases are $120$

Total outcomes are 17$c_{3}$$=680$ ways

Probability is defined as the ratio of possible outcomes to number of outcomes.

$=120/680$

$=3/17$

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