Answer :
bit strings of length 12 contain a) exactly three 1s is 220 b) at most three 1s is 2700 c) atleastthree1s is 220 d) an equal number of 0s and 1s is 66.
a) To calculate the number of bit strings of length 12 containing exactly three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3).The solution is 12C3 = 220.
b) To calculate the number of bit strings of length 12 containing at most three 1s, we can use the summation formula. The formula is sum of nCr, where n is the total number of bits (12) and r is the number of 1s (3). So, the answer is (12C0 + 12C1 + 12C2 + 12C3) = 2700.
c) To calculate the number of bit strings of length 12 containing at least three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3). The solution is 12C3 = 220.
d) To calculate the number of bit strings of length 12 containing an equal number of 0s and 1s, we can use the combination formula. The formula is nCr
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