Question

You are selecting 10 numbers randomly out of the first 100 odd numbers. Sum of these 10 odd numbers is

a. How many different values of a are possible?

Answer 1

the values of a can ve infinite in number because a line has infinite points

Answer 2

Answer:

Step-by-step explanation:

The first 100 odd natural numbers are 1,3,5,....199.  Let the total different values be A

If we take any set of 10 numbers their sum will lie between a minimum value of 1+3+5+..19 i.e 100 and the maximum value of 181 + 183 + ...+ 199. i.e 1900

Then difference between these two numbers is 1800. Since all intermediate numbers will appear in steps of 2. Hence there are 900 intermediate numbers.

Also we will include minimum number i.e 100, which we haven't added yet since we subtracted (10 - 1 doesn't include 1 in list )

Hence in all there are 901 sums i.e 901 A's.