A company has $10$ employees. The company has decided to form a team including atleast three employees and also excluding atleast three employees. Then the number of ways of forming the team is $k,$ then unit digit of $k$ is

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Solution

Required number of ways of forming the team is summation of selecting 3 members out of 10 to selecting 7 members out of 10 $=^{10} C_{3} +^{10} C_{4} +^{10} C_{5} + . . . . +^{10} C_{7} = 2^{10} - (^{10} C_{0} +^{10} C_{1} +^{10} C_{2} +^{10} C_{8} +^{10} C_{9} +^{10} C_{10}) = 2^{10} - 2 \times (1 + 10 + 45) = 912$

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