Question

How many non empty collections are possible by using 5 P's and 6 Q's ?​

Answer 1

Answer:

41

Step-by-step explanation:

5p -ppppp

6q -qqqqqq

assume ,

we have also added empty set

eg - if there is no p

then q q q q q q

if there in no q

p p p p p

so there will be 6 ways of writing p and

7 ways of writing q

so

6 × 7 = 42 but in que we want only non empty collection

then 42 -1 = 41

Answer 2

42 non-empty collections are possible by using 5 P's and 6 Q's.

Given,

5 P's and 6 Q's

To Find,

The number of possible non-empty collections =?

Solution,

We can solve the question as follows:

It is asked that we have to find the number of non-empty collections possible from 5 P's and 6 Q's.

A non-empty collection will contain a minimum of 1 and a maximum of 11 letters.

The number of times we can select P is = 0,1,2,3,4,5

The number of times we can select Q is = 0,1,2,3,4,5,6

Now,

The total number of ways in which we can select both P and Q is:

6*7 = 42

Since one of the set will contain 0 P and 0 Q, we will subtract 1.

Therefore,

Non-empty collections possbile = 42 - 1 = 41

Hence, 42 non-empty collections are possible by using 5 P's and 6 Q's.

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