And now if you want to say well what about for the three chairs? Well for each of these 30 scenarios, how many different people could you put in chair number three? Well you're still going So you have a total of 30 scenarios where you have seated six You have five scenarios for who's in chair number two. Someone in chair number one and for each of those six, Or another way to think about it is there's six scenarios of So that means you haveįive out of the six people left to sit in chair number two. Scenarios we've taken one of the six people to Now for each of those six scenarios, how many people, how many different people could sit in chair number two? Well each of those six There are six people whoĬould be in chair number one. We put in chair number one? Well there's six different And we can say look if no one's sat- If we haven't seated anyone yet, how many different people could Permutations of putting six different people into three chairs? Well, like we've seen before, we can start with the first chair. But it'll be very instructive as we move into a new concept. This is covered in the permutations video. One, chair number two and chair number three.
Out all the scenarios, all the possibilities,Īll the permutations, all the ways that we could Video, we're going to say oh we want to figure Person B, we have person C, person D, person E, and we have person F. About different ways to sit multiple people in Number of Combinations: The number of all combinations of n things, taken r at a time is:Ĭ r n = n ! ( r ! ) ( n - r ) ! = n n - 1 n - 2. Note that AB and BA represent the same selection.Įx.2 : All the combinations formed by a, b, c taking ab, bc, ca.Įx.3 : The only combination that can be formed of three letters a, b, c taken all at a time is abc.Įx.4 : Various groups of 2 out of four persons A, B, C, D are : AB, AC, AD, BC, BD, CD.Įx.5 : Note that ab ba are two different permutations but they represent the same combination.
Then, possible selections are AB, BC and CA. Combinations: Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.Įx.1 : Suppose we want to select two out of three boys A, B, C.
Then, number of permutations of these n objects is : Important Result: If there are n subjects of which p1 are alike of one kind p2 are alike of another kind p3 are alike of third kind and so on and pr are alike of rth kind, number of all permutations of n things, taken all at a time = n!. Number of Permutations: Number of all permutations of n things, taken r at a time, is given by: Permutations: The different arrangements of a given number of things by taking some or all at a time, are called permutations.Įx1 : All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).Įx2 : All permutations made with the letters a, b, c taking all at a time are:( abc, acb, bac, bca, cab, cba) Then, factorial n, denoted n! is defined as: n!=n(n - 1)(n - 2). Factorial Notation: Let n be a positive integer. FACTS AND FORMULAE FOR PERMUTATIONS AND COMBINATIONS QUESTIONSġ.
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