The board of directors of a corporation must select a president, a secretary, and a treasurer. in how many possible ways can this be accomplished if there are 21 members on the board of directors?

7980 ways

Step-by-step explanation:

When select predident:21 ways

When select secretary: 20 ways

When select treasurer: 19 ways

It is permutation

N permutation r=NPR

20permutation3=21×20×19= 7980 ways

7980 ways

Step-by-step explanation:

Pretty simple.

we are finding variation.

Variation = N factorial/ (N-P)factorial/

N = the total number of elements we have available

P = the number of elements out of n we need to select

N = 21

P = 3

Variation = 21 factorial/(21-3)factorial = 21 factorial/ 18 factorial

Variation = 21x20x19x 18factorial/ 18 factorial

Variation = 21x20x19 = 7980 possible ways of selecting 3 positions out of a board of 21 members.

is it clear?

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this