In how many different ways can a ski club consisting of 20 people select a person for its officers? the positions available are president, vice president, treasurer, and secretary. no person can hold more than one positions and the each office is filled in order.
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a)74
b) 116,280
c) 1440
d) 4845

D. 4845ways

Step-by-step explanation:

Combination has to do with selection.

To select r object from pool of n objects, this can be expressed using the combination formula

nCr = n!/(n-r)!r!

According to the question, total number of people in the ski club is 20 i.e n=20

If the positions available are president, vice president, treasurer, and secretary, this shows that we need to select 4people to from the pool of 20 to fill the positions. This can be done in 20C4 number of ways.

20C4 = 20!/(20-4)!4!

20C4 = 20!/16!4!

20C4 = 20×19×18×17×16!/16!×4×3×2×1

20C4 = 20×19×18×17/24

20C4 = 4845

This can be done in 4845ways

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%