Question

1. Find the number of 5 letter words that can be formed using the letters of the word CONSIDER.
How many of them begin with "C", how many of them end with "R", and how many of them begin
with "C" and end with "R"?

Answer 1

1.

$8\cdot7\cdot6\cdot5\cdot4=6720$

begin with "C"

$1\cdot7\cdot6\cdot5\cdot4=840$

end with "R"

$7\cdot6\cdot5\cdot4\cdot1=840$

begin with "C" and end with "R"

$1\cdot6\cdot5\cdot4\cdot1=120$

Answer 2

Answer:

Step-by-step explanation:

total no. of letters... c, o, n, s, i, d, e, r

total no. of letters which can be formed..

6720

letters starting with c:

lets have 5 blanks

_ _ _ _ _  1 * 7 * 6* 5* 4

on first place a letter c.. then for second space we have 7 letters.. for third 6 letters remain.. then for 2nd 5 letters and for last blank we have 4 letters to choose from..

so multiplying all..

or we can write as

1* 7C8 * 6C7* 5C6 * 4C5

= 840

ENDING WITH R..

same process like above

fix letter r at last and then consider how many letters are available for each blank..

answer will be...

840

ENDING WITH R AND STARTING WITH C

fix r and c at last and first respectively

then

c _ _ _ r  

then same as first..

we have 6 letters for 2nd,  5 for 3rd and 4 for 4th blank

answer:

120