A5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. find the probability of guessing the correct combination if: a. no digit is repeated b. digits can repeat and zero is not one of the digits in the combination (can this be done in fraction form? ! )

A. 5 digit code with digits from 0-9 with no repetition.

Choices for 1st digit=10, and choices for successive digits are 9,8,7,6.

Probability of guessing it correctly on first try is

1/(10*9*8*7*6) = 1/30240

B. If zero is not in the combinations, then the domain of digits is 1-9, or 9 choices. Digits can repeat means every digit in the code has 9 choices.

Number of arrangements = 9^5 = 59049

Probability of guessing at first try = 1/59049

A.


B.

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

quit

step-by-step explanation: