Permutation and combination

[maleeha2882]

In how many ways can the letters of the word FACETIOUS be arrangrd in a line ?
What is the probability that an arrangement begins with F and S ?

 

[robinhoodmustafa]

In how many ways can the letters of the word FACETIOUS be arrangrd in a line ?
What is the probability that an arrangement begins with F and S ?

No restriction so
First part: 9!

2nd part (Not sure but do check)
8! * 8!

 

[Rutzaba]

9!

wats the ans to prt two ? 1/81

 

[PhyZac]

First is 9! = 362880

Second is 2! x 7! = 10080

 

[Rutzaba]

First is 9! = 362880

Second is 2! x 7! = 10080

dude it says probability

 

[PhyZac]

dude it says probability

Opps!

10080/362880 = 1/36

 

[maleeha2882]

9!

wats the ans to prt two ? 1/81

no, its 1/72..

 

[robinhoodmustafa]

Opps!

10080/362880 = 1/36

Explain me the second part. Pls

 

[PhyZac]

Explain me the second part. Pls

I did it wrong actually,

I thought the probability with F and S in the beginning.

The answer 1/72, but I am still trying to figure out how.

 

[robinhoodmustafa]

O

I did it wrong actually,

I thought the probability with F and S in the beginning.

The answer 1/72, but I am still trying to figure out how.

Ok

 

[Kumkum]

I did it wrong actually,

I thought the probability with F and S in the beginning.

The answer 1/72, but I am still trying to figure out how.

First is 9! = 362880

Second is 2! x 7! = 10080

ok i'll try and explain this
the first part is fine 9!
the second part is only 7!, see here u need to fix F and S since it should begin with these two letters so,
FS _ _ _ _ _ _ _
so u have 7 empty places and u can arrange them in 7! ways
hence probability = 7!/9! = 1/72

PhyZac it can't be 2! x 7! because the question says both letters should be at the beginning(and i guess it doesn't matter which letter u start with as long as F and S are at the beginning)
but if it said F or S then u wud have 8! x 2
because
F _ _ _ _ _ _ _ _ or
S _ _ _ _ _ _ _ _
i don't know if i've helped but hope u get it...

 

[PhyZac]

Kumkum
Thank you soooo much!! Jazaki Allah Khairan, I got the your point! May Allah S.W.T reward you, and bless you with highest grades, Ameen!!

 

[Kumkum]

Kumkum
Thank you soooo much!! Jazaki Allah Khairan, I got the your point! May Allah S.W.T reward you, and bless you with highest grades, Ameen!!

Ameen.
not a problem nd Wa iyyakum. May Allah s.w.t help u with ur exams as well and may u get the best grades, Ameen

 

[Rutzaba]

ok i'll try and explain this
the first part is fine 9!
the second part is only 7!, see here u need to fix F and S since it should begin with these two letters so,
FS _ _ _ _ _ _ _
so u have 7 empty places and u can arrange them in 7! ways
hence probability = 7!/9! = 1/72

PhyZac it can't be 2! x 7! because the question says both letters should be at the beginning(and i guess it doesn't matter which letter u start with as long as F and S are at the beginning)
but if it said F or S then u wud have 8! x 2
because
F _ _ _ _ _ _ _ _ or
S _ _ _ _ _ _ _ _
i don't know if i've helped but hope u get it...

the question wasnt clear it starting with f and s could have meant several things :/

 

[Kumkum]

the question wasnt clear it starting with f and s could have meant several things :/

yes...the question confused me too...but i think that's how you do it...