In general the number of selections (Combinations) from a total of n objects taking r objects at a time is denoted by n Cr. There are 3 selections possible from a total of 3 objects taking 2 objects at a time and we write 3C2= 3. In how many ways 2 varieties can be selected? The possible selections areĮach such selection is known as a combination. Let us consider 3 plant varieties V1, V2 & V3. The word selection is used, when the order of thing is immaterial. Therefore number of arrangements required = 5040 -1440 = 3600.Ĭombination means selection of things. Number of arrangements in which all varieties of jasmine are together = 1440. Ii)The number of arrangements of all 7 varieties without any restrictions =7! = 5040 Hence the total number of arrangements required In every one of these permutations, 2 varieties of jasmine can be rearranged among themselves in 2! ways. This together with 5 varieties of roses make 6 units which can be arranged themselves in 6! ways. I) Since the 2 varieties of jasmine are inseparable, consider them as one single unit. (ii)All varieties of jasmine are not together. In how many ways can they be arranged, if There are 5 varieties of roses and 2 varieties of jasmine to be arranged in a row, for a photograph. Therefore 6 varieties of brinjal can be arranged in 720 ways.Ĥ. Six varieties of brinjal can be arranged in 6 plots in 6P6 ways. There are 6 varieties on brinjal, in how many ways these can be arranged in 6 plots which are in a line? In general the number of permutations of n objects taking r objects at a time is denoted by nPr. Therefore from Fundamental Counting Principle the total number of ways in which both the boxes can be filled is 3 x 2 =6. After filling the first box we are left with only 2 objects and the second box can be filled by any one of these two objects. Since we want to arrange only two objects and we have totally 3 objects, the first box can be filled by any one of the 3 objects, (i.e.) the first box can be filled in 3 ways. How many arrangements are possible? For this consider 2 boxes as shown in figure. Suppose out of the 3 objects we choose only 2 objects and arrange them. Thus there are 6 arrangements (permutations) of 3 plants taking all the 3 plants at a time. These 3 plants can be planted in the following 6 ways namelyĮach arrangement is called a permutation. Let us assume that there are 3 plants P1, P2, P3. The word arrangement is used, if the order of things is considered. If there are n jobs and if there are mi ways in which the ith job can be done, then the total number of ways in which all the n jobs can be done in succession ( 1st job, 2nd job, 3rd job… nth job) is given by m1 x m2 x m3 …x mn. The above principle can be extended as follows. Since there are 3 road routes from Coimbatore to Chennai, the total number of routes is 3 x 4 =12. This can be explained as follows.įor every route from Coimbatore to Chennai there are 4 routes from Chennai to Hyderabad. Then the total number of routes from Coimbatore to Hyderabad via Chennai is 3 x 4 =12. Assume that there are 3 routes (by road) from Coimbatore to Chennai and 4 routes from Chennai to Hyderabad. If a first job can be done in m ways and a second job can be done in n ways then the total number of ways in which both the jobs can be done in succession is m x n.įor example, consider 3 cities Coimbatore, Chennai and Hyderabad. MATHS:: Lecture 16 :: PERMUTATION AND COMBINATION
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