Explanation
Step 1:FindingnumberofwordsstartingwiththealphabetsinthegivenwordStep 1:Findingnumberofwordsstartingwiththealphabetsinthegivenword
No. of words beginning with A =4!=4×3×2=24No. of words beginning with A =4!=4×3×2=24
No. of words beginning with N =4!=4×3×2=24No. of words beginning with N =4!=4×3×2=24
No. of words beginning with R =4!=4×3×2=24No. of words beginning with R =4!=4×3×2=24
No. of words beginning with U =4!=4×3×2=24No. of words beginning with U =4!=4×3×2=24
So, in total 96 words will be formed while beginning with letter A, N, R and U.So, in total 96 words will be formed while beginning with letter A, N, R and U.
Step 2:FindingtheorderofthewordStep 2:Findingtheorderoftheword
Order of 97 th word − VANRUOrder of 97 th word − VANRU
Order of 98th word − VANUROrder of 98th word − VANUR
Order of 99th word − VARNUOrder of 99th word − VARNU
Order of 100th word− VARUN.Order of 100th word− VARUN.
Therefore,rankofword′VARUN′is 100. Option C is correct.Therefore,rankofword′VARUN′is 100. Option C is correct.
Step -1: Simplifying the problem.Step-1: Simplifying the problem.
13C2+13C3+......+13C13.13C2+13C3+......+13C13.
=13C0+13C1+13C2+13C3+......+13C13−13C0−13C1.=13C0+13C1+13C2+13C3+......+13C13−13C0−13C1.
=(13C0+13C1+13C2+.....+13C13)−(13C0+13C1) →(i).=(13C0+13C1+13C2+.....+13C13)−(13C0+13C1) →(i).
Step -2: Deduce the value of (13C0+13C1+13C2+.....+13C13) using summation formula. Step -2:Deduce the value of (13C0+13C1+13C2+.....+13C13) using summationformula.
n∑i=0nCi=2n →(ii)∑i=0nnCi=2n →(ii)
⇒(13C0+13C1+13C2+.....+13C13)=13∑i=013Ci.⇒(13C0+13C1+13C2+.....+13C13)=∑i=01313Ci.
⇒13∑i=013Ci=213(By using (ii)).⇒∑i=01313Ci=213(By using (ii)).
then, using (i) and (ii) we get,then,using (i) and (ii) we get,
∴213−(13C0+13C1).∴213−(13C0+13C1).
=213−(13!13!0!+13!12!1!).=213−(13!13!0!+13!12!1!).
=213−(1+13).=213−(1+13).
=213−14.=213−14.
Hence , the correct answer is (B) 213−14.Hence , the correct answer is (B) 213−14.
We have,
A box contains pair of shoes =5=5
Selected pair of shoes =4=4
Then,
Exactly one pair of shoes obtained is
=5P4=5P4
=5!(5−4)!=5!(5−4)!
=5!1!=5!=5!1!=5!
=5×4×3×2×1=5×4×3×2×1
=120=120
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