Respuesta :
By using the concept of Permutations and Combinations, the Counting Principle president, a vice-President, and the secretary of the club can be chosen in 990 ways.
Permutations and Combinations are about making arrangements and making selections on the basis of certain formulas
The re-arranging of any given given data which is sorted in some ordered way is called a permutation. The “permutation” word actually tells us that change the linear order of the ordered set.
Selecting items from a huge source of items without taking any care about their order is called combinations.
We need to choose three members out of 11 members. So here we use a combination. So selecting r things from n things we can do selection in ncr ways, so we can choose of members in 11c1×10c1×9c1 ways
We know that ncr is equivalent to [tex]\frac{n!}{r!(n-r)!}[/tex]
So, using this concept total number of ways to select a member of a club
=((11c1)×(10c1)×(9c1))
=11×10×9
=990 ways
Hence president, vice president and secretary can be selected by 990 ways
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