The planning committee at school has 10 members. exactly four of these members are teachers. a four-person subcommittee with at least one member who is a teacher must be formed from the members of the planning committee. how many distinct subcommittees are possible?

865

Step-by-step explanation: The set of possibilities are:

Subcommittee  is of 4 people according to:

4  teachers    0 other member       total possibilities    1

3  teachers     1     teachers  C₄,₃  = 4   and  other member  6    6*4   =  24

2 teachers     2      C₄,₂  =  4!/2!  = 12    2 (om)    and  C₆,₂   =  6!/4!  = 30

30*12  = 360

1  teacher        3     (om)               4         and  C₆,₃ = 6!/3!   =  120

120*4  = 480

Total ways of committee    1  + 24  + 360 +  480  = 865

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.