How many different 3 digit odd numbers are possible if repeated digits are allowed?
Question 1123457: the number of three-digit odd numbers with no repeated digits is: A) 280 B) 320 C) 336 D) 360 E) 405 Found 2 solutions by greenestamps, ikleyn: Answer by greenestamps(11265)  You can put this solution on YOUR
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(1) The units digit has to be odd: how many choices? (2) The hundreds digit can't be 0; and it can't be the same as the units digit: how many choices? (3) The tens digit can't be the same as either the units digit or the hundreds digit: how many choices? By the fundamental counting principle, the number of 3-digit numbers with the specified restrictions is the product of the numbers of choices for each digit. Answer by ikleyn(46435) You can put this solution on YOUR website! this number = 8*5 + 7*8*5 = 40 + 280 = 320.
First addend 8*5 corresponds to the numbers having one of the digits {1, 3, 5, 7 ,9} as the last (ones) digit
and 0 (zero) as the middle digit.
Second addend 7*8*5 corresponds to the numbers having one of the digits {1, 3, 5, 7 ,9} as the last (ones) digit;
any different non-zero at the middle position and any different from these two non-zero digit at the most-left position.
In mathematics, permutation is known as the process of arranging a set in which all the members of a set are arranged into some series or order. The process of permuting is known as the rearranging of its components if the set is already arranged. Permutations take place, in more or less important ways, in almost every area of mathematics. They frequently appear when different commands on certain finite sets are considered. What is a Combination? A combination is an act of choosing items from a group, such that (not like permutation) the order of choice does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the union of n things taken k at a time without repetition. In combination, you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used. Permutation Formula In permutation r things are selected from a set of n things without any replacement. In this order of selection matter.
Combination Formula In combination r things are selected from a set of n things and where the order of selection does not matter.
How many 3-digit even numbers can be formed by using the digits 1,2,3,4, and 5?Solution:
Similar QuestionsQuestion 1: How many 3 digit odd numbers can be formed by using the digits 1,2,3,4 and 5? Solution:
Question 2: How many 4 digit even numbers can be formed by using the digits 1,2,3,4 and 5? Solution:
How many 3Hence, the number of 3-digit odd numbers that can be formed = 3×4×5= 60. (ii) When repetition of digits is allowed: Again, the unit's place can be filled up by 1, 3, 5. that is, in 3 ways. But the ten's and hundred's place can be filled up by any of the 6 given digits in 6 ways each. (since repetition is allowed)
How many possible numbers with no digit repeated?The first digit can be 1, 2, 3, 4, 5, 6, 7, 8, or 9. The second digit can be any of the remaining 9 numbers, and the 3rd digit can be any of the remaining 8 numbers. So, 9 * 9 * 8 = 648 possible numbers with no digit repeated.
How many digits are there in a number?We have three digits. Since the number should be odd, the last digit should be one of those numbers $1, 3, 5, 7, 9$. Now the second digits can be one of the digits: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ There are 10 different digits for the second digits, but since the digits should be different we cannot place 10 digits, but we can place 9 digits.
When repetition of digits is not allowed?(ii) repetition of digits is allowed? (i) When repetition of digits is not allowed: Since we have to form a 3-digit odd number, thus the digit at unit's place must be odd. Hence, the unit's place can be filled up by 1, 3 or 5, that is, in 3 ways.
How many three digit odd numbers are there if repetition is allowed?Hence, the number of 3-digit odd numbers that can be formed =3×6×6=108.
How many 3 digit numbers are possible if the number is odd?The three digit numbers are 100 to 999 inclusive so there are 999-100+1 = 999-99 = 900 So, 900 three digit numbers If half of all numbers is odd then half of 900 is 450, there are 450 odd positve 3 digit numbers.
How many 3 digit combinations are there with repeats?There are 6 = 3x2x1 ways to order 3 digits in a row. Thus the number of combinations of 3 of the 10 digits is 720/6 = 120 combinations.
How many 3 digit numbers that are odd can be formed whose digits are distinct?Thus there are 60, 3 digit numbers, with distinct digits, with each of the digits odd. Note: We should be very careful about multiplying those numbers.
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