State whether the following statements are true or false and also give the reason in support of your answer:

(a) 

(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.

(c) While analysing the data of a 5 × 5 Latin Square design the d.f. for ESS is equal to 16

(d) In a Two-way Analysis of Variance test with 5 observations per cell having 4 blocks and 4 treatments the degree of freedom for the total variation is 64.

(e) The probability of selection of a sample of n from the population by SRSWOR is 1/ N

(b) True
Reason: The total number of all possible samples of size 3 without replacement from a population of size 7 is given by the combination formula:

7C3=7!3!(7−3)!=7×6×53×2×1=35^7C_3 = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

So the statement is False (not True as mentioned).
Correct answer: False
Reason: Total number of samples = (73)=35\binom{7}{3} = 35, _______ _____ ______ ___ ___ _______.
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