Question

The letters of the word FLOWER are taken 4 at a time and arranged in all
possible ways. Find the number of arrangements that
a. Begins with F and ends with R .
b. Contain the letter E.

Answer 1

Answer:

Since F and R occupy first and the last position, we can select any two letters out of the remaining four.

These can be done in

4

C

2

ways

i.e.

n

C

r

=

(n−r)!r!

n!

=

(4−2)!2!

4!

=

2!2!

4!

=

2!2!

4×3×2×1

=6

These 2 selected letters can be arranged themselves in 2 ways.

Total number of ways =6×2=12

Hence, the answer is option C.