ધારો કે S એ GARDEN શબ્દના બધા અક્ષરોને ગોઠવીને બનાવી શકાય તેવા તમામ શબ્દોનો ગણ છે. ગણ S માંથી, એક શબ્દ યાદૃચ્છિક રીતે પસંદ કરવામાં આવે છે. પસંદ કરેલા શબ્દમાં સ્વરો મૂળાક્ષરોના ક્રમમાં ન હોય તેની સંભાવના શું છે?

A \(\frac{1}{2}\)
B \(\frac{1}{4}\)
C \(\frac{2}{3}\)
D \(\frac{1}{3}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

A, E,G R D N \(\text { Probabllity }(\mathrm{P})=\frac{\text { favourable case }}{\text { Total case }}\) (when A & E are in order) Total case \(=6\) ! Favourable case \(={ }^6 \mathrm{C}_2 .4\) ! \(P=\frac{(15) 4!}{(30) 4!}\) Probablity when not in order…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

વર્ગ	\(5-10\)	\(10-15\)	\(15-20\)	\(20-25\)	\(25-30\)	\(30-35\)
આવૃત્તિ	\(2\)	\(k\)	\(28\)	\(54\)	\(k+1\)	\(5\)

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