A bag contains 50 tickets numbered 1, 2, 3, 4.....50 of which five are drawn at random and are arranged in ascending order of magnitude. Find the probability that third drawn ticket is equal to 30.
a) 551/15134
b) 1/2
c) 551/15379
d) 1/9
e) 1/50
We are picking 5 distinct numbers. If we want to arrange them in increasing order there's one way to do that per selection.
To ensure that 30 comes right in the middle 2 numbers should be smaller than 30 and two greater than 30.
The two smaller numbers can be picked in 29C2 ways out of 1 - 29.
The two greater numbers can be picked in 20C2 ways out of 31 - 50.
The 5 numbers can be chosen out of 50 in 50C5 ways.
Hence the total probability of (desired) / (total outcomes) = (29C2 * 20C2) / 50C5 = (29*28*20*19)*5! / (50*49*48*47*46)*2*2 = 551/15134
A.
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A quick refresher
nCr formula is used to find the number of ways where r objects are chosen from n objects and the order they exist in is not important. It is represented in the following way.
Here,
- n is the total number of things.
- r is the number of things to be chosen out of n things.
Let us learn the NCR formula along with a few solved examples below.
John has to choose 5 marbles from a larger group of 12 marbles. In how many ways can she choose them?
Solution:
Choose 5 out of 12 marbles.
As order doesn't matter (marbles aren't mentioned to be different from one another) so we use the nCr formula.
Thus he can choose it in ways
2 comments:
This explanation presents the probability problem in a very systematic way by breaking it into combinations and showing why order matters only after the numbers are selected. The walkthrough makes it easy to understand why 30 must be the median value, requiring exactly two smaller and two larger tickets. The additional refresher on the nCr formula is also helpful for readers who want to strengthen their combinatorics fundamentals before tackling similar aptitude questions.
Students preparing for competitive examinations can benefit from practicing more problems involving combinations, permutations, and probability alongside IEEE Projects of CSE, as analytical thinking and structured problem-solving are valuable across many technical disciplines. Developing a strong mathematical foundation improves reasoning skills that are useful in both academics and software-related careers.
Mastering concepts such as combinations, probability distributions, and logical reasoning also complements exploring Domains in Computer Engineering. Building confidence in mathematical analysis enables students to approach algorithm design, optimization, and data-driven problem solving with greater clarity and precision.
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