MathDB

2017 Combinatorics #10: Number of Words

Source:

February 20, 2017

Problem Statement

Compute the number of possible words

w=w_1w_2\dots w_{100}

satisfying:

\bullet

w

has exactly

50

A

's and

50

B

's (and no other letter).

\bullet

For

i=1,2,\dots,100

, the number of

A

's among

w_1, w_2, \dots, w_i

is at most the number of

B

's among

w_1, w_2, \dots, w_i

.

\bullet

For all

i=44,45,\dots,57

, if

w_i

is a

B

, then

w_{i+1}

must be a

B

.

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