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Question 30 of 44

Q.(A) Find the probability of getting P in the first place in all possible arrangements of each and every letter of the word PUJAN.

(OR)
(B) Find the probability of having 5 Tuesdays in the month of August of a leap year.
Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2023Subjective· 4mImportance★★★★★
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(A) Fix P first: 4!5!=15\frac{4!}{5!}=\frac15. OR (B) 31-day month has 3 extra weekdays; Tuesday is 5 times if it is among the first 3 days: 37\frac37.

Part (A): The word PUJAN has 55 distinct letters, so total arrangements =5!=120=5!=120. If P is fixed in the first place, the remaining 44 letters can be arranged in 4!=244!=24 ways.

P(P first)=4!5!=24120=15=0.2.P(\text{P first})=\frac{4!}{5!}=\frac{24}{120}=\frac{1}{5}=0.2.

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