Combinatorics quiz

The number of ways of placing r distinct objects into n non-distinct cells with no cell left empty is equal to

• S(r, n)

• n!

• P(n, r)

• C(n,r)

S(r, n) is called the Stirling number of

• first kind

• second kind

• third kind

• fourth kind

__________ is the summing operator of the ordinary generating function.

• 1 / (1 - x)

• 1 / (1 + x)

• e^x

• 1 / e^x

Tags

CCSS.HSA.SSE.B.4

The coefficient of the term x^20 in (1 - 3 x^2 + 4 x^7 + 12 x^21 - 5 x^45) / ( 1- x)

• 2

• 14

• 9

• -2

Tags

CCSS.HSA.SSE.B.4

The ordinary enumerator of the selection of r objects out of n objects with unlimited repetition is

• C( n + r - 1, r)

• C(n, r)

• P(n, r)

• S (n, r)

C(n, 0) + C(n, 1) + C(n, 2) + . . . + C(n, n) =

• 2 ^ n

• n ^ 2

• n !

• n^n

Commutative is not satisfied in

• permutation

• combination

The exponential generating function of the sequence {P(0,0), P(2,1), P(4, 2), …, P(2r, r)…} is

• ( 1 – 4x) ^ (–½ )

• ( 1 + 4x) ^ (–½ )

• ( 1 – 4x) ^ (½ )

• ( 1 + 4x) ^ (½ )

The exponential generating function of the sequence {1, 1, 1,…, 1,…}

• e^x

• e^(-x)

• 1/(1+x)

• 1/(1-x)

Tags

CCSS.HSF.LE.A.2

The exponential enumerator for the permutation of a single object with no repetition is

• 1

• 1 + x

• (1+x) ^ 2

• 1/ (1 +x)

Tags

CCSS.HSA.APR.C.5