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JEE Main 20208 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2020 · 8 January · Evening Shift · Mathematics · Permutation and Combination

The number of 4 letter words (with or without meaning) that can be...

The number of 44 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATIONEXAMINATION is

Correct answer

2454

Step-by-step solution

EXAMINATIONEXAMINATION
2N,2A,2I,E,X,M,T,O2N, 2A, 2I, E, X, M, T, O
Case I:I: All are different, so 8P4=8!4!=8⋅7⋅6⋅5=1680{}^{8}{P}_{4} = \dfrac{8 !}{4 !} = 8 \cdot 7 \cdot 6 \cdot 5 = 1680
Case II:II: 22 same and 22 different, so 3C1C274!2!=3⋅21⋅12=756{}^{3}{C}_{1} C2 7 \dfrac{4 !}{2 !} = 3 \cdot 21 \cdot 12 = 756
Case III:III: 22 same and 22 same, so 3C24!2!2!=3⋅6=18{}^{3}{C}_{2}\dfrac{4 !}{2 ! 2 !} = 3 \cdot 6 = 18
Total number of words=1680+756+18=2454= 1680 + 756 + 18 = 2454
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