(C) The total number of ways to arrange $6$ distinct people in a row is $6! = 720$.In any arrangement of these $6$ people,there are $4! = 24$ possible

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(C) The total number of ways to arrange $6$ distinct people in a row is $6! = 720$.In any arrangement of these $6$ people,there are $4! = 24$ possible relative orders for the specific individuals $A, B, C,$ and $D$.Out of these $24$ possible relative orders,only $1$ order satisfies the condition that they appear in the sequence $ABCD$.Therefore,the number of favorable arrangements is $\frac{6!}{4!} = \frac{720}{24} = 30$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In how many ways can $6$ people be arranged in a row such that $A, B, C,$ and $D$ always appear in the order $ABCD$ (not necessarily together)?

A
$4$
B
$10$
C
$30$
D
$720$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In how many ways can $6$ people be arranged in a row such that $A, B, C,$ and $D$ always appear in the order $ABCD$ (not necessarily together)?

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