Consider the 10 -digit number M=9876543210 . We obtain a new 10-digit number from M according to the following rule: we can choose one or more disjoint pairs of adjacent digits in M and interchange the digits in these chosen pairs, keeping

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Consider the 10 -digit number M=9876543210 . We obtain a new 10-digit number from M according to the following rule: we can choose one or more disjoint pairs of adjacent digits in M and interchange the digits in these chosen pairs, keeping the remaining digits in their own places. For example, from M=9876343210 , by interchanging the 2 underlined pairs, and keeping the others in their places, we get M₁=9786453210 . N

Quantrex Academy · Accepted Answer

Correct answer: 88

Number of ways if single pair is changed =9= ^9 C₁ Number of ways if 2 pairs changed =7+6+5+ +1=28= ^8 C₂ Number of ways if 3 pairs changed = ^7 C₃ So, total numbers that can be formed = ^9 C₁+ ^8 C₂+ ^7 C₃+ ^6 C₄+ ^5 C₅ aligned & =9+28+35+15+1 & =88 aligned

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