Given a number of digit cards namely 3, 8, and 9. What is the probability of a 3 -digit odd number being generated using all the cards?
Answers
Answer:
The Probability of a Pair of 8s
Our final goal is to determine the probability of finding any pair of adjacent
numbers, but a bit of preparation is required.
We will start by looking for a pair of a specific number, say, 8. There are 52
cards altogether, and the laws of permutations tell us that there are 52! ways
of arranging them. 52! is a big number.
52! ≈ 8.066 × 1067
There are 4 rank 8 cards, and 52C4 tells us the number of ways that these
4 cards can be positioned within a 52-card deck. This is calculated as follows.
52C4 =
52!
(52 − 4)!4! = 270725
After these four cards have been removed from the deck, there are 48 cards
left. We’ll represent those cards using a | character (Figure 1).
| | | | | | | | | | | | | | | | · · · · · · · · · · · · | |
| | | | 8 | | | 8 | | 8 | | | · · · · · · · · · · · · | 8 | | | | |
Figure 1. The probability of no adjacent 8s
Step-by-step explanation:
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12/24 is the probability