Out of 10 persons P1, P2,..., P10, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. The number of such arrangements is ___________.
Since out of 5 to be selected, P1 is fix i.e P1 must occur.
⇒ we need to select 4 person out of 9 remaining.
Now, out of remaining 9, P4 and P5 do not occur
⇒ Available options are 7
⇒ Number of such arrangement
= 7C4 × 5! (since 5 persons in line can be arranged in 5! ways.)
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