Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter. In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered. Permutation Formula In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.
Combination A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, order doesn’t matter 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. Combination Formula In combination r things are picked from a set of n things and where the order of picking does not matter.
How many 4 digit numbers can be formed by using the digit 1 to 9. If repetition of digits is not allowed?Answer:
Similar QuestionsQuestion 1: How many 5 digit numbers can be formed by using the digit 1 to 9. If repetition of digits is not allowed? Answer:
Question 2: How many 3 digit numbers can be formed by using the digit 0,1,2,3. If repetition of digits is allowed? Answer:
Question 3: How many 5 digit numbers can be formed by using the digit 0,1,2,3,4. If repetition of digits is allowed? Answer:
Question 4: How many 4 – digit even numbers can be formed using the digits (3,5,7,9,1,0) if repetition of digits is not permitted? Answer:
Text Solution 302430009*9*9None of these Answer : A Solution : For the first digit place there are 9 options , second digit place there are 8 options, third digit place there are 7 options and fourth digit place there are 6 options.<br> so number of 4 digit numbers=`9 xx 8 xx 7xx6=3024`<br>
Work backwards... There are two cases, either the units digit is $0$ or $5$. If it ends in $0$, then the tens digit can be $1-9$, 9 possibilities, the hundreds digit can be the remaining $8$, and the thousands can be the remaining $7$. So the total is $9\cdot 8\cdot 7$. Note then if you start with $5$ in the units place, you approach the same way, however, the thousands digit can not be $0$ (why?). So the total then is $8\cdot 8\cdot 7$. Now what do you do with both of these numbers? |