Match List-I with List-II

List-I	List-II
(A) The number of different words that can be formed with CUSTOM with the condition that the word should begin with M is ______.	(I) 70
(B) The number of different ways in which the letters of the word EXTRA can be arranged so that the vowels are never together is ______.	(II) 45
(C) There are 10 points in a plane. No three of these points are in a straight line. The total number of straight line that can be formed by joining the two points is _______.	(III) 72
(D) The number of ways a committee of 4 people be chosen out of 8 people is _______.	(IV) 120

Choose the correct answer from the options given below:

(A) Words starting with M from CUSTOM

Word CUSTOM has 6 letters: C, U, S, T, O, M

M is fixed at the first position. The remaining 5 letters need to be arranged.

Remaining letters: C, U, S, T, O

Number of ways $= 5!$

$= 5 \times 4 \times 3 \times 2 \times 1$

$= 120$

(A) matches with (IV) 120

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(B) Arranging EXTRA so vowels are never together

Word EXTRA has 5 letters

Vowels: E, A (2 vowels)

Consonants: X, T, R (3 consonants)

Total arrangements $= 5! = 120$

For arrangements where vowels ARE together, treat (EA) as one unit.

Units to arrange: (EA), X, T, R (4 units)

Arrangements of 4 units $= 4! = 24$

E and A can swap within the unit $= 2! = 2$

Arrangements with vowels together $= 24 \times 2 = 48$

Arrangements with vowels never together $= 120 - 48$

$= 72$

(B) matches with (III) 72

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(C) Straight lines from 10 points (no 3 collinear)

10 points are available with no 3 points in a straight line.

A line requires 2 points. Order doesn't matter.

Number of lines $= C(10,2)$

$= \dfrac{10!}{2! \times 8!}$

$= \dfrac{10 \times 9}{2}$

$= 45$

(C) matches with (II) 45

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(D) Committee of 4 people from 8 people

Total people: 8

Need to choose: 4

Order doesn't matter for a committee.

Number of ways $= C(8,4)$

$= \dfrac{8!}{4! \times 4!}$

$= \dfrac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}$

$= \dfrac{1680}{24}$

$= 70$

(D) matches with (I) 70

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Final Matching:

List-I	List-II
(A) CUSTOM starting with M	(IV) 120
(B) EXTRA vowels never together	(III) 72
(C) Lines from 10 points	(II) 45
(D) Committee of 4 from 8	(I) 70

Correct Answer: (A) - (IV), (B) - (III), (C) - (II), (D) - (I)