A teacher has to choose the maximum number of different groups comprising of four students from a total of six students. Of these groups, in how many groups will one particular student be a part of?Choices:- 10 20 15 17
Question
A teacher has to choose the maximum number of different groups comprising of four students from a total of six students. Of these groups, in how many groups will one particular student be a part of?Choices:- 10 20 15 17
Solution
To solve this problem, we can use the concept of combinations in mathematics.
Step 1: We need to find the total number of groups of 4 students that can be formed from 6 students. This can be calculated using the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
So, C(6, 4) = 6! / [(6-4)! * 4!] = 15.
Step 2: Now, we need to find the number of groups in which one particular student will be a part of. This means we are now choosing 3 students from the remaining 5 (since one student is already chosen).
So, C(5, 3) = 5! / [(5-3)! * 3!] = 10.
Therefore, one particular student will be a part of 10 different groups. So, the correct answer is 10.
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