QPaperGen

First note the letters in PERMUTATIONS:

Total letters = 12

Vowels = E, U, A, I, O → 5 vowels (all distinct)

Consonants = P, R, M, T, T, N, S → 7 consonants, with T repeated twice

✅ Step 1: Treat all vowels as one block

Group the 5 vowels into a single unit:

(E U A I O)

Now instead of 12 separate letters, we have:

1 vowel block + 7 consonants = 8 total items

But among the consonants, T repeats twice.

Number of ways to arrange these 8 items:

8
!
2
!
2!
8!
​


(Since the two T's are identical.)

✅ Step 2: Arrange the 5 vowels within the block

All 5 vowels are distinct, so they can be arranged among themselves in:

5
!
5!
✅ Final Answer
8
!
2
!
×
5
!
2!
8!
​

×5!
​


Now compute:

8
!
=
40320
8!=40320

2
!
=
2
2!=2 →
8
!
/
2
!
=
40320
/
2
=
20160
8!/2!=40320/2=20160

5
!
=
120
5!=120

So total arrangements:

20160
×
120
=
2419200
20160×120=2419200

✅ Final Answer:

2
,
 ⁣
419
,
 ⁣
200
2,419,200
​