COMEDK2012MathematicsPermutation and Combination
If 2 9 ! + 2 3 ! 7 ! + 1 5 ! 5 ! = 2^ a b ! , where a, b N , then the ordered pair (a, b) is
Options
- A(10,9)
- B(10,7)
- C(9,10)
- D(5,10)
Correct answer
C. (9,10)
Step-by-step solution
We have, aligned & 2 9 ! + 2 3 ! 7 ! + 1 5 ! 5 ! = 2^ a b ! & 1 9 ! [2+ 2 8 9 3 ! + 6 7 8 9 5 ! ]= 2^ a b ! & 1 9 ! [2+24+ 126 5 ]= 2^ a b ! & 1 9 ! [26+ 126 5 ]= 2^ a b ! & 1 9 ! [ 256 5 ]= 2^ a b ! & 1 9 ! 256 2 5 2 = 512 10 ! = 2⁹ 10 ! = 2^ a b ! a=9 and b=10 aligned