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  1.  A set S has 5 elements. How many ways we can choose subsets P and Q ,so that P intersection Q is null.?
  2. A fruit salad can be made using at least one of the fruits mango, apple, pineapple, watermelon and banana. How many varieties os salad possible?
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Anonymous 0 Comments

answer 1

first we can select a set for P and then for Q

6 cases will occur:

case 1: P is NULL set then Q can have 2^5 options.ways=2^5

case 2: p contains set with 1 element i.e. 5c1 and q will contain 2^4(we will remove the element given to p and count the no. of subsets formed with remaining 4 elements).ways=5*2^4

similarly

case 3: ways=5c2*2^3

case 4:ways=5c3*2^2

case 5: ways=5c4*2^1

case 6: ways=5c5*2^0(complete set and null set).

total ways=sum all the six cases.

plz correct if wrong.

 

answer 2:

we can select atleast 1 from five different fruits

no. of ways=5c1+5c2+5c3+5c4+5c5=2^5-1

or we can say every fruit has 2 choices i.e 2^5 .We remove the choice when none is selected so total ways=2^5-1

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