Problem: Find the number of ways in which a person can choose one or more of the four electrical appliances: T.V, Refrigerator, Washing Machine, and a cooler.

Solution:

To solve this problem, we can use the concept of combinations. A combination is a way of selecting items from a larger set without regard to the order of the items.

Step 1: Find the number of ways to choose one appliance.
There are four appliances to choose from, so there are 4 ways to choose one appliance.

Step 2: Find the number of ways to choose two appliances.
There are four appliances to choose from for the first choice, and three appliances left to choose from for the second choice. However, since the order of the choices doesn't matter, we need to divide by 2 to avoid overcounting. So the number of ways to choose two appliances is (4 x 3) / 2 = 6.

Step 3: Find the number of ways to choose three appliances.
There are four appliances to choose from for the first choice, three appliances left for the second choice, and two appliances left for the third choice. However, since the order of the choices doesn't matter, we need to divide by 3 x 2 = 6 to avoid overcounting. So the number of ways to choose three appliances is (4 x 3 x 2) / (3 x 2) = 4 x 3 = 12.

Step 4: Find the number of ways to choose four appliances.
There is only one way to choose all four appliances.

Step 5: Add up the results from Steps 1-4 to get the total number of ways.
Total number of ways = 4 + 6 + 12 + 1 = 23.

Therefore, the correct answer is (d) none of these, as none of the given options match the answer we obtained. The correct answer is 23.

Here, the person can chose one or more appliances out of four:
so, 1st case: 4c1 = 4 ,2nd = 4c2 = 6, 3rd = 4c3 = 4 and last he can chose 4c4 = 1
now , add the four selection= 4+6+4+1= 15
the correct option is (a)