# Q2 (2 marks)

Subject: Natural Language Processing

Exam: M2

Reader: https://deep-learning-study-room.vercel.app/nlp/#m2/mocks/mock-c/q2

Canonical: https://deep-learning-study-room.vercel.app/read/nlp/m2/mocks/mock-c--q2/

M2 · confirmed 2 + 2 + any two of 3 + 3 + 3 · worked practice

### Q2

Each of five words may receive any of three POS tags. How many possible tag sequences exist before applying constraints? (2 marks)

**Given**

T=5 token positions; K=3 choices at each position.

**To find**

Total tag sequences.

### Formula and why it applies



$$
K^T
$$



Choose one tag independently for each position when counting candidates; multiply the number of options five times.

### Solution

#### Step 1. Expand the power



$$
3^5=3\times3\times3\times3\times3
$$



#### Step 2. Multiply



$$
3\times3=9,\quad9\times3=27
$$





$$
27\times3=81,\quad81\times3=243
$$



243 tag sequences.