# Statistics combination question

You are in charge of creating a “USELESS” committee. The committee shall consist of one Umpire, three Statisticians, two Electricians, and one Lawyer (get it?). You personally know two Umpires, five Statisticians, three electricians, and four lawyers. Unfortunately, one of the Statisticians and one of the Electricians refuse to work together. How many USELESS committees can you create?

The answer given to me was 144.

what i did was 208 = (combination of not having both) + (combination removed one statistician) + (combination removing one electrician)

=[(4c1)(2c2)(4c3)(2c1)]+[(4c1)(3c2)(4c3)(2c1)]+[(4c1)(2c2)(5c3)(2c1)]

=32+96+80 =208

Thank you

$$\binom21_U \binom 53_S \binom32_E \binom 41_L - \binom21_U \binom42_S \binom 21_E \binom 41_L$$