1. Determine the number of permutations of {1,2, ., 8} in which exactly four integers are i their natural positions. (for example 18365472 is a good permutation because a1 = 1, a3 3, az = 5, a7 =7 and the other four integers 2,4,6,8 are not in their natural position.) 2. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a nonzero, even number of times. Uint, wnite the onotino funetien onmino the onr
1. Determine the number of permutations of {1,2, ., 8} in which exactly four integers are i their natural positions. (for example 18365472 is a good permutation because a1 = 1, a3 3, az = 5, a7 =7 and the other four integers 2,4,6,8 are not in their natural position.) 2. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a nonzero, even number of times. Uint, wnite the onotino funetien onmino the onr
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Determine the number of permutations of {1,2, ..., 8} in which exactly four integers are in
their natural positions. (for example 18365472 is a good permutation because a1 = 1, az =
3, az = 5, a7 =7 and the other four integers 2,4,6,8 are not in their natural position.)
2. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a
nonzero, even number of times.
Hint: write the appropriate exponential generating function and then determine the n-th term
through it.
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