The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is . Given 8

Question

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is . Given 8 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

N → 2, A → 2, I → 2, E, X, M, T, O → 1 Category Selection Arrangement 2alikeof one kind and 2 alike of other kind 3C2 = 3 3× (4!/2! 2!) = 18 2 alike and 2 different 3C1 × 7C2 3C1×7C2× (4!/2!) = 756 All 4 different 8C4 8C4 × 4! = 1680 Total = 2454

Category	Selection	Arrangement
2alikeof one kind and 2 alike of other kind	$^{3} C_{2} = 3$	$3 \times \frac{4 !}{2 ! 2 !} = 18$
2 alike and 2 different	$^{3} C_{1} \times^{7} C_{2}$	$^{3} C_{1} \times^{7} C_{2} \times \frac{4 !}{2 !} = 756$
All 4 different	$^{8} C_{4}$	$^{8} C_{4} \times 4! = 1680$

Q. The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is __________. Given 8

N→2,A→2,I→2,E,X,M,T,O→1 Category Selection Arrangement 2alikeof one kind and 2 alike of other kind 3C2​=3 3×2!2!4!​=18 2 alike and 2 different 3C1​×7C2​ 3C1​×7C2​×2!4!​=756 All 4 different 8C4​ 8C4​×4!=1680 Total =2454

Q. The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is __________.
Given 8