The number of permutations by using all the digits of the number 986754 which niether begins with 8 nor ends with 5 is λ , then the value of λ2 is
A
180
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B
210
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C
690
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D
252
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Solution
The correct option is D252 Let set A= numbers begining with 8 and
set B= numbers ending with 5
Now we have to find A′∩B′ ∵A′∩B′=(A∪B)′ n(A∪B)′=n(U)−n(A∪B) n(A∪B)=n(A)+n(B)−n(A∩B)
Now, n(A∪B)′=n(U)−[n(A)+n(B)−n(A∩B)]=6!−[5!+5!−4!]⇒λ=504∴λ2=5042=252