7.3: 8 There are 12 hospitals in a town. How many different ways can seven patie

Question

7.3: 8 There are 12 hospitals in a town. How many different ways can seven patients be sent to the hospitals so that no two patients may be in the same hospital? 7.4: 8 A box contains 15 apples. How many different selections of 3 apples can be made so as to include a particular apple? 7.6: 2 Find the coefficient of x3 y4 in the expansion of ( x+2y 7 7.8: 4 Three distinct coins are tossed. List all possible outcomes in the sample space. List the outcomes in the event E that two coins show heads only. What is the probability of obtaining exactly two heads? 8.1: 6 Find the recurrence relation and initial conditions for the sequence S : 2, 4, 10, 28,..., 3n+,.

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Q7.3.8) There are 12 hospitals in town. How many different ways can 7 patients be sent to hospitals so that no 2 patients are in the same hospital?

Answer)

So there are 12 hospitals in the town.

Now, 7 patients be sent to hospitals so that no 2 patients are in the same hospital.

We can think the problem in this way that we have to choose 7 hospitals among 12 and each patient will be in each hospital.

The above can be done in:

C(n,r)=n!/(r!(n?r)!) ways

= 12!/(7!(12?7)!)

= 792 ways.

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