Question

Plzzzzzzzz! A suitcase lock has a code 4 symbols long. The symbols on the lock are a star, a square, a circle, a triangle, a line, and a pentagon. What is the probability that a randomly chosen code starts with a star followed by triangle and doesn't contain the same symbol twice? Enter your answer as a fraction in simplest form.

Answer 1

Answer:

                $\dfrac{1}{30}$

Step-by-step explanation:

6 symbols and 4-symbol code so number of combinations wich doesn't contain the same symbol twice would be:

6•5•4•3 = 360

If code starts with a star followed by triangle that means only one posibility for first two symbols and code doesn't containing the same symbol twice means that left 4 symbols for next two.

So number of combinations of code starting with a star followed by triangle and doesn't containing the same symbol twice will be:

1•1•4•3 = 12

The probability that a randomly chosen code starts with a star followed by triangle and doesn't contain the same symbol twice:

$\dfrac{1\cdot1\cdot4\cdot3}{6\cdot5\cdot4\cdot3}=\dfrac{1\cdot1}{6\cdot5}=\dfrac{1}{30}$