Hello Student,

First of all the word is ENGINEER.

Let total ways of arranging this word are A

Now A = 8! / 3! * 2! ;   A = 3360

Now let all E are taken together as a single unit , i.e. now total words in engineer left are 6.

Let ways of arranging now the word with all E together are B

So B = 6! / 2! :  B = 360

Now probability of getting all E together is given by P.

P = B/A  = 3/28

Hello Student,

combine all E's together in one group and consider it as a single unit

now there are 6 groups

arranging 6 groups in all possible ways = 6!/2!

[divide by 2! coz N's are repeated]=360

total no. of ways = 8! / [3! * 2!]=3360

prob = 360/3360=36/336=0.107

Hope i was able to answer your question.

Hello,

consider [EEE]  it as a one block to be permuted along with NGINR
favorable ways = 6!/2! = 360
total ways = 8!/3!2! = 3360
Pr = 360/3360 = 3/28

Generally, This type  of questions can be solved  like a dice question, what's the probability of rolling a 1 on a 6 sided dice, 1/6
Engineer is an 8 letter word and there are 3 E's, so 3/8.