How many digit number greater than 200 but less than 300 can be obtained from 1234,and what is the probability that a number choosen at random falls into this range
If 200<n<300, then the first digit must be 2. That leaves 4 digits for each of the remaining digits for a total of m=1*4*4*4 numbers.
If there is no limitation, the number of all possible (distinct) numbers is
N=4^4.
The probability that a number formed by the digits 1,2,3,4 will fall into that range is therefore m/N.
To find the number of digit numbers greater than 200 but less than 300 that can be obtained from 1234, we need to consider the smallest and largest possible numbers.
The smallest possible number greater than 200 formed using the digits of 1234 is 213. The largest possible number less than 300 is 234.
To calculate the probability that a number chosen at random falls into this range, we can count how many numbers fall into this range and divide it by the total number of possible outcomes.
Counting the numbers from 213 to 234, we see that there are 22 numbers in the desired range.
To find the total number of possible outcomes, we need to consider that we can arrange the digits of 1234 in different ways to form different numbers. Since 1234 has four distinct digits, there are 4! = 4 × 3 × 2 × 1 = 24 possible arrangements.
Therefore, the probability that a number chosen at random falls into the desired range is 22/24 = 11/12 or approximately 0.92.
To find the number of digits between 200 and 300 that can be obtained from the digits 1, 2, 3, and 4, we need to consider the possible combinations.
The digit in the hundreds place can only be 2, since we want a number greater than 200. So we have one digit fixed: _ _ 2.
The tens place can be filled by any of the four remaining digits (1, 3, or 4) since there are no restrictions. So now we have two digits filled: _ _ 2.
The units place can also be filled by any of the remaining three digits (1, 3, or 4) since there are no restrictions. So we have three digits filled: _ _ 2.
Therefore, the number of possible three-digit numbers between 200 and 300 that can be obtained from the digits 1, 2, 3, and 4 is 3 × 4 × 1 = 12.
The total number of four-digit numbers that can be formed using these four digits is 4 × 4 × 3 × 2 = 96.
To find the probability that a randomly chosen number falls into the range between 200 and 300, divide the number of favorable outcomes (12) by the total number of possible outcomes (96):
12 / 96 = 1 / 8.
So the probability that a number chosen at random falls into the range between 200 and 300 is 1/8, or 0.125 (12.5%).