Question

How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} keyboard_arrow_down Solution (b) The alphabet {a, b, c}

Answer 1

Answer:

Part (A) The required ways are 792.

Part (B) The required ways are 101376.

Step-by-step explanation:

Consider the provided information.

Part (A) The alphabet {a, b}

The length of strings is 12 that containing exactly five a's.

The number of ways are: $\frac{12!}{5!7!}$

After filling "a" we have now 7 places.

For 7 places we have "a" and "b" alphabet but we already select a's so now the remaining place have to fill by "b" only.

Thus, the required ways are: $\frac{12!}{5!7!}\times 1=792$

Part (B) The alphabet {a, b, c}

We have selected five a's now we have now 7 places.

For 7 places we have "b" and "c".

Thus, there are 2 choices for each 7 place that is $2^7$

Therefore the total number of ways are: $792\times 2^7=101376$

Thus, the required ways are 101376.