Question

How many 10-bit strings contain 6 or more 1’s? Explain and show all the steps.

Answer 1

Number of strings with 6 1's: $C_{10}^6=\frac{10!}{6!4!}=210.$

Number of strings with 7 1's: $C_{10}^7=\frac{10!}{7!3!}=120.$

Number of strings with 8 1's: $C_{10}^8=\frac{10!}{8!2!}=45.$

Number of strings with 9 1's: $C_{10}^6=\frac{10!}{9!1!}=10.$

Number of strings with 10 1's: $C_{10}^{10}=\frac{10!}{10!0!}=1.$

Number of strings with 6 or more 1's: $N=210+120+45+10+1=386.$