How many different permutations can you make with the letters in the word seventeen?

1 Answer
Jul 27, 2018

Answer:

#" "#
A total of

#color(red)(7560# permutations are possible

with the letters in the word #color(blue)("Seventeen"#.

Explanation:

#" "#
We can use the following formula:

If there are #color(red)(n# objects with #color(blue)(r# types, then

#color(red)((n!)/("n_1 ! n_2 ! n_3 ! n_4 ! ...... n_r !)#

The word given is : #color(green)("Seventeen"#

Observe that there is a total of #color(red)(9# alphabets in the word.

The letter #color(blue)("S"# appears #color(red)(1# time

The letter #color(blue)("E"# appears #color(red)(4# times

The letter #color(blue)("V"# appears #color(red)(1# time

The letter #color(blue)("N"# appears #color(red)(2# times

The letter #color(blue)("T"# appears #color(red)(1# time

We can calculate the different permutations as follows:

#color(blue)(["9 ! "]/("1 ! 4 ! 1 ! 2 ! 1 !")#

#rArr ["9 ! "]/("1 * 24 * 1 * 2 * 1 )#

#rArr (362,880)/48#

#rArr 7560#

Hence,

A total of #color(red)(7560# permutations are possible

with the letters in the word #color(blue)("Seventeen"#.

Hope it helps.