We start with 6, and count down by 1 each time we fill up a slot. We stop once the third slot is filled or accounted for. The countdown is to ensure that we don't pick the same person twice. From here, multiply those values: 6*5*4 = 30*4 = 120

Interestingly, this is equal to 5! = 5*4*3*2*1 = 120 because the 3*2 becomes 6 and that *1 at the end doesn't affect things. Though usually results of permutation problems don't always end up like this. The order matters because a result like ABC is different from BAC, where A,B,C,D,E,F are the six school organizations.

As a slightly longer way to do the problem, you can use the nPr formula which is $_nP_r = \frac{n!}{(n-r)!}$ where n = 6 and r = 3 in this case. The exclamation marks indicate factorial. If you go this route, you should find that one of the steps will involve 6*5*4.

4 0

3 years ago

Sorin hits a cricket ball straight up into the air. After 1.5s, the ball is falling straight down with a speed of 6.5 m/s. We wa

sveticcg [70]

Step-by-step explanation:

We have, Sorin hits a cricket ball straight up into the air. After 1.5 s, the ball is falling straight down with a speed of 6.5 m/s.

We want to find the initial vertical velocity of the ball.

The relation between initial speed, final speed, acceleration and time is given by using first equation of kinematics. Let v₀ is the initial speed. So,

$v=v_o +at$

Here, v = -6.5 m/s, t = 1.5 s and a = -g

$v_o=v-at\\\\v_o=v+gt\\\\v_o=-6.5+9.8\times 1.5\\\\v_o=8.2\ m/s$

So, the initial velocity of the ball is 8.2 m/s and the formula used is (1).

4 0

4 years ago