For a string of binary digits of length bits, how many strings are there with at least Four and at least Four .
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A string of binary digits of length 1 1 bits with at least four 0 's and four 1 's has three bits leftover that could be either all three 0 's, two 0 's and one 1 , two 1 's and one 0 , or all three 1 's. These have the following total number of different anagrams:
0 0 0 0 1 1 1 1 0 0 0 → 7 ! 4 ! 1 1 ! = 3 3 0
0 0 0 0 1 1 1 1 0 0 1 → 6 ! 5 ! 1 1 ! = 4 6 2
0 0 0 0 1 1 1 1 0 1 1 → 6 ! 5 ! 1 1 ! = 4 6 2
0 0 0 0 1 1 1 1 1 1 1 → 7 ! 4 ! 1 1 ! = 3 3 0
for a total of 2 ( 3 3 0 + 4 6 2 ) = 1 5 8 4 different strings.