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The Question & Answer (Q&A) Knowledge Managenet

The Internet has many places to ask questions about anything imaginable and find past answers on almost everything.

Table of Contents

- How do you find the combination?
- How many combinations of 49 numbers are there?
- How do you find the number of possible outcomes?
- How do you find the probability of outcomes?
- What is possible outcomes?
- What are the chances of guessing a 3 digit code?
- What are the chances of guessing a 10 digit code?
- What is the probability that you will get a 3 digit combination correct if no digits in the combination can be repeated?
- What is the probability of guessing a 4 digit code?
- What is the probability that two digit number selected at random will be multiple of 3 and not a multiple of 5?
- What is the probability of getting a two digit number from 1 to 30?
- What is the probability that a randomly chosen 2 digit number is divisible by 3?
- How many two digit numbers which are multiples of 3?

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! * (n – r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

13,983,816

The fundamental counting principle is the primary rule for calculating the number of possible outcomes. If there are p possibilities for one event and q possibilities for a second event, then the number of possibilities for both events is p x q.

How to calculate probability

- Determine a single event with a single outcome.
- Identify the total number of outcomes that can occur.
- Divide the number of events by the number of possible outcomes.

Possible Outcomes – a list of all the resulting possibilities from an event. e.g. When rolling a die – all possible outcomes are 1, 2, 3, 4, 5, 6. 6. Favorable Outcome – the result that is desired. e.g. Roll a 4 on a die → 4 is the only favorable outcome.

If you include the one and 2 digit integers with enough zeros prepended to make them 3 digit, then your possibilities range from 000 to 999, which would give you 1,000 different 3-digit integers. With that your chances of guessing the right one would be 1/1000 or 0.001.

As a straightforward simple example, if you have a 10 digit (0-9) keypad that will unlock after a 4 digit PIN is entered (and this is known) then the chances are 1 in 10 4, or 1 in 10,000.

What is the probability that you will get a 3-digit combination correct if no digits in the combination can be repeated? 1/10.

How easy would it be for a thief to guess your four-digit PIN? If he were forced to guess randomly, his odds of getting the correct number would be one in 10,000—or, if he has three tries, one in 3,333.

24 out of the 90 two digit numbers are divisible by ‘3’ and not by ‘5’.

Therefore, the favorable cases are 30–6=24. >> Hence, the required probability is 24/90 = 4/15.

Thus, there are 90 such numbers. Since out of these, 30 numbers are multiple of 3, therefore, the probability that a randomly chosen positive 2-digit integer is a multiple of 3, is 30/90 = 1/3.

2 digit numbers which are multiples of 3: 12, 15, 18, 21, …, 90, 93, 96, 99. Consider this A.P. : a = 12, d = 3, 99 = 12 + (n- 1) (3) => n – 1 = 87/3 = 29 => n = 30. There are 30 multiples of 3 in all 2 digit numbers.