Ascending tickets: GMAT Quant Probability

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 12C512C5 ways