4 numbers are drawn at random from 10 tiles numbered 0-9. what are the odds of drawing numbers 1-4 in any order.
the question is confusing me
the prob you will pick a correct first number = 4/10
the prob that the second one is correct = 3/9
etc
so the prob of drawing a 1,2,3, and 4
= (4/10)(3/)(2/8)(1/7) = 1/210
or
total number of ways of 'choosing' 4 specifics form 10 is C(10,4) = 210
only one of these will be the correct choice we want.
so prob = 1/120
line << = (4/10)(3/)(2/8)(1/7) = 1/210 >>
should read
= (4/10)(3/9)(2/8)(1/7) = 1/210
and it looks like a transposed the digits in the last line
so prob = 1/210
Odds are different from probability, therefore, the odds would be 1:9 for each one. You can only pull a 2 out of the bag of 9 different tiles once. Same goes for the rest of the numbers.
To calculate the odds of drawing numbers 1-4 in any order from 10 tiles numbered 0-9, you can use the concept of permutations and combinations. Let me explain step by step how to calculate it:
Step 1: Determine the total number of possible combinations of drawing 4 numbers from 10 tiles without any restrictions. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
In this case, n is the total number of tiles (10) and r is the number of tiles drawn (4). Substituting the values, we get:
C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!)
Step 2: Determine the number of combinations that include the numbers 1, 2, 3, and 4 in any order. Since any of the 4 numbers can be in any position, the number of combinations is the same as the total number of permutations of these 4 numbers. This can be calculated using the permutation formula:
P(n, r) = n!
In this case, n is the total number of distinct numbers (4). Substituting the value, we get:
P(4, 4) = 4!
Step 3: Calculate the odds by dividing the number of combinations that include numbers 1-4 in any order by the total number of possible combinations:
Odds = (Number of Combinations with 1-4) / (Total Number of Combinations)
Odds = P(4, 4) / C(10, 4)
Simplifying this expression, we have:
Odds = 4! / (10! / (4! * 6!))
Now, you can calculate this expression using a calculator or by simplifying the factorials further. Once you have the odds, you can express them as a fraction or convert them to a decimal or percentage.