How many bit strings of length 10 have more 0s than 1s?

Case A = there are 10 zeros and no ones
Case B = there are 9 zeros and 1 one
Case C = there are 8 zeros and 2 ones
Case D = there are 7 zeros and 3 ones
Case E = there are 6 zeros and 4 ones

Any other case isn't possible since we want more 0s than 1s



For case A, we have 10 C 0 = 1 way to do this which is just a string of 0s, which is length 10. The notation 10 C 0 refers to the n C r combination formula. 

For case B, we have 10 C 1 = 10 ways to do this. Simply move the lone 1 to be placed at each slot giving 10 different combinations.

For case C, we have 45 different combos because 10 C 2 = 45. 

Case D has 120 different outcomes (note how 10 C 3 = 120)

Case E has 210 different outcomes (10 C 4 = 210)

As a shortcut, you can look at Pascal's triangle. Look at the row that starts with 1, 10, 45, ... and record the first 5 values. Those values match up with the results we got.



Now add up those results to get: 1+10+45+120+210 = 386

Therefore, the final answer is 386. There are 386 different bit strings of length 10 that has more 0s than 1s.

There would be 36.35 pounds

The volume is 56.8 triangular the