A family has just moved to a new city and requires the services of both an obstetricianand a pediatrician. There are two easily accessible medical clinics, each havingtwo obstetricians and three pediatricians. The family will obtain maximum healthinsurance benefits by joining a clinic and selecting both doctors from that clinic.In how many ways can this be done? Denote the obstetricians by O1, O2, O3, andO4 and the pediatricians by P1,…, P6. Then we wish the number of pairs (Oi, Pj)for which Oi and Pj are associated with the same clinic. Because there are fourobstetricians, n1 5 4, and for each there are three choices of pediatrician, so n2 5 3.Applying the product rule gives N 5 n1n2 5 12 possible choices.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
A family has just moved to a new city and requires the services of both an obstetrician
and a pediatrician. There are two easily accessible medical clinics, each having
two obstetricians and three pediatricians. The family will obtain maximum health
insurance benefits by joining a clinic and selecting both doctors from that clinic.
In how many ways can this be done? Denote the obstetricians by O1, O2, O3, and
O4 and the pediatricians by P1,…, P6. Then we wish the number of pairs (Oi, Pj)
for which Oi and Pj are associated with the same clinic. Because there are four
obstetricians, n1 5 4, and for each there are three choices of pediatrician, so n2 5 3.
Applying the product rule gives N 5 n1n2 5 12 possible choices.
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